Subgroups — #34090121

Order 19792.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₄₇₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#23754706	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₁₂₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₂₃₇	—	2	1	no	—
5	C₄×C₁₂₃₇	C₂²	1	1	yes	characteristic
6	Dic₁₂₃₇	—	2	1	no	—
7	C₂×C₁₂₃₇	—	4	1	no	—
8	C₂×C₁₂₃₇	D₄	1	1	yes	characteristic
9	C₁₂₃₇	SD₁₆	1	1	yes	characteristic, complemented, Sylow
10	SD₁₆	—	1237	1	no	maximal, Sylow
11	Q₈	—	1237	1	no	—
12	D₄	D₁₂₃₇	1	1	yes	characteristic
13	C₈	—	1237	1	no	—
14	C₂²	—	2	1	no	—
15	C₄	—	2474	1	no	—
16	C₄	C₂×D₁₂₃₇	1	1	yes	characteristic
17	C₂	—	4	1	no	—
18	C₂	C₂²⋊D₁₂₃₇	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.