Subgroups — #14557372

Order 2368.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₉₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₉₂	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₄₈	—	2	1	no	—
5	D₂₉₆	—	2	1	no	—
6	C₁₆×C₃₇	C₂²	1	1	yes	characteristic
7	D₁₄₈	—	4	1	no	—
8	Dic₇₄	—	4	1	no	—
9	C₈×C₃₇	D₄	1	1	yes	characteristic
10	C₂×D₃₇	—	8	1	no	—
11	C₄×C₃₇	D₈	1	1	yes	characteristic
12	Dic₃₇	—	8	1	no	—
13	C₂×C₃₇	D₁₆	1	1	yes	characteristic
14	D₃₇	—	16	1	no	—
15	SD₆₄	—	37	1	no	maximal, Sylow
16	C₃₇	SD₆₄	1	1	yes	characteristic, complemented, Sylow
17	Q₃₂	—	37	1	no	—
18	D₁₆	—	37	1	no	—
19	C₃₂	D₃₇	1	1	yes	characteristic, complemented
20	Q₁₆	—	74	1	no	—
21	D₈	—	74	1	no	—
22	C₁₆	C₂×D₃₇	1	1	yes	characteristic
23	Q₈	—	148	1	no	—
24	D₄	—	148	1	no	—
25	C₈	D₁₄₈	1	1	yes	characteristic
26	C₂²	—	296	1	no	—
27	C₄	—	296	1	no	—
28	C₄	D₂₉₆	1	1	yes	characteristic
29	C₂	—	592	1	no	—
30	C₂	D₅₉₂	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.