Subgroups — D₆₈₄₈ #28334674

Order 13696.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₄₂₄	C₂	1	2	yes	maximal, complemented
2	C₆₄×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₇₁₂	—	2	2	no	—
4	C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
5	D₈₅₆	—	4	2	no	—
6	C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
7	D₄₂₈	—	8	2	no	—
8	C₈×C₁₀₇	D₈	1	1	yes	characteristic
9	C₂×D₁₀₇	—	16	2	no	—
10	C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
11	C₂×C₁₀₇	D₃₂	1	1	yes	characteristic
12	D₁₀₇	—	32	2	no	—
13	D₆₄	—	107	1	no	maximal, Sylow
14	C₁₀₇	D₆₄	1	1	yes	characteristic, complemented, Sylow
15	D₃₂	—	107	2	no	—
16	C₆₄	D₁₀₇	1	1	yes	characteristic, complemented
17	D₁₆	—	214	2	no	—
18	C₃₂	C₂×D₁₀₇	1	1	yes	characteristic
19	D₈	—	428	2	no	—
20	C₁₆	D₄₂₈	1	1	yes	characteristic
21	D₄	—	856	2	no	—
22	C₈	D₈₅₆	1	1	yes	characteristic
23	C₂²	—	1712	2	no	—
24	C₄	D₁₇₁₂	1	1	yes	characteristic
25	C₂	—	3424	2	no	—
26	C₂	D₃₄₂₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.