In Chapter 3, the Gnat tells Alice about the different insects she is seeing. Their names are playful portmanteaus, and one in particular is an allusion to a popular Victorian party game that is unfamiliar to most modern readers:
“Look on the branch above your head,” said the Gnat, “and there you’ll find a Snap-dragon-fly. Its body is made of plum-pudding, its wings of holly-leaves, and its head is a raisin burning in brandy.”
The "Snap-dragon-fly" combines the words "dragonfly" and "snap-dragon." A snapdragon is a kind of plant, but that is not what the Gnat is referencing. "Snap-dragon" was also the name of a game in which Victorians filled a shallow bowl with brandy, floated raisins in it, and lit the brandy on fire. Players were then supposed to scramble to snatch the raisins out of the brandy and eat them. Part of the fun was for players to hold flaming raisins in their mouths so that they looked like dragons or demons. The game sounds dangerous (and it was), but the way alcohol burns also meant that it was possible to play the game without getting hurt.
Snap-dragon was popular during holidays, and in one version, the flaming raisins surrounded a whole Christmas or holiday pudding. Given the Gnat's description of the Snap-dragon-fly, this is likely the version Alice has played or has seen played. This allusion is one of many clues that the Looking-Glass World is an invention of Alice's imagination. The novel is set just before Guy Fawkes Day in November, and she is looking forward to the festivities on the horizon. Her dream is not just a philosophical critique of the real world's nonsense, but also a reflection of a little girl's excitement for the revelry that happens when adults take a break from all that nonsense.
In Chapter 6, Alice walks toward an egg on a shelf that she has purchased from the Sheep. The egg itself is anthropomorphized in the novel and is an allusion to a poem Alice knows:
However, the egg only got larger and larger, and more and more human: when she had come within a few yards of it, she saw that it had eyes and a nose and mouth; and, when she had come close to it, she saw clearly that it was HUMPTY DUMPTY himself. “It ca’n’t be anybody else!” she said to herself. “I’m as certain of it, as if his name were written all over his face!”
Humpty Dumpty is still a well-known nursery rhyme character today. At the time Carroll was writing, there were many versions of the poem about Humpty Dumpty circulating, largely by word-of-mouth. In fact, the poem started as a riddle about what Humpty Dumpty was (the answer was "an egg"). This is one of the more dream-like experiences Alice has while moving across the chess board. The egg is not Humpty Dumpty to begin with, but rather transforms impossibly before her eyes from a regular chicken egg into a human-like creature with "eyes and a nose and mouth." This is the kind of impossible transformation that can only happen in the imagination. What's more, as they begin to speak, Alice is able to start reciting the version of the Humpty Dumpty story she knows. Like other characters Alice meets (the Kings, Queens, and Knights, Haigha and Hatta), Humpty Dumpty alludes to something familiar to Alice outside of the Looking-Glass World. This is not just an instance of Carroll inserting an allusion to a riddle into the story for the reader's benefit, but also of Alice's imagination inserting an allusion into her own dream. The way Carroll—and Alice herself—is able to make ideas and inanimate objects come alive in the Looking-Glass World suggests an affinity between writers and imaginative children. This affinity is yet another example of a looking-glass inversion: children can imagine entire worlds around themselves, and writers are constantly striving to be as powerful at imagination as they are.
In Chapter 7, Alice, the White King, Haigha, and Hatta hear the Lion and the Unicorn fighting. This fight is a satirical allusion to the political history of England and Scotland:
“Why, the Lion and the Unicorn, of course,” said the King.
“Fighting for the crown?”
“Yes, to be sure,” said the King: “and the best of the joke is, that it’s my crown all the while! Let’s run and see them.”
And they trotted off, Alice repeating to herself, as she ran, the words of the old song:—
Alice immediately asks if the Lion and the Unicorn are fighting for the crown because these are the words to a nursery rhyme she knows. The nursery rhyme refers to the unification of England and Scotland. In 1603, King James VI of Scotland became King James I of England after Queen Elizabeth I died, ending the Tudor line of succession to the English throne. The lion traditionally represents England, and the unicorn traditionally represents Scotland. Alice is eager to see the fight and better understand the rhyme.
The Lion and the Unicorn in Through the Looking-Glass are fighting not for the English crown, but rather for the White King's crown. As the White King tells Alice, this fight is a joke. The Lion and the Unicorn are both on the White King's side of the board, so this is basically a pointless civil war. Carroll uses this joke to satirize U.K. politics, at least among England and Scotland. The Lion has a clear physical advantage, even though the Unicorn seems smarter. The Lion's brute strength suggests that the English empire is absurdly strong and that, regardless of politics, it will always have an advantage over Scotland. It does not matter greatly (at least according to Carroll) who gets the crown because the Lion will remain, effectively, in charge. This is not necessarily a patriotic commentary; the Lion does not come out of the chapter looking especially good, and there are no real morals to the fight between the Lion and the Unicorn. Instead, Alice walks away with the sense that the fight the nursery rhyme is based on is no more logical than the silly rhyme itself.