Subgroups — #32973900

Order 18688.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₃₃₆	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₆₇₂	C₂	1	1	yes	maximal, characteristic
3	C₇₃×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₁₆₈	—	2	1	no	—
5	D₂₃₃₆	—	2	1	no	—
6	C₆₄×C₇₃	C₂²	1	1	yes	characteristic
7	Dic₅₈₄	—	4	1	no	—
8	D₁₁₆₈	—	4	1	no	—
9	C₃₂×C₇₃	D₄	1	1	yes	characteristic
10	Dic₂₉₂	—	8	1	no	—
11	D₅₈₄	—	8	1	no	—
12	C₁₆×C₇₃	D₈	1	1	yes	characteristic
13	D₂₉₂	—	16	1	no	—
14	Dic₁₄₆	—	16	1	no	—
15	C₈×C₇₃	D₁₆	1	1	yes	characteristic
16	C₂×D₇₃	—	32	1	no	—
17	C₄×C₇₃	D₃₂	1	1	yes	characteristic
18	Dic₇₃	—	32	1	no	—
19	SD₂₅₆	—	73	1	no	maximal, Sylow
20	C₂×C₇₃	D₆₄	1	1	yes	characteristic
21	D₇₃	—	64	1	no	—
22	Q₁₂₈	—	73	1	no	—
23	D₆₄	—	73	1	no	—
24	C₁₂₈	D₇₃	1	1	yes	characteristic, complemented
25	C₇₃	SD₂₅₆	1	1	yes	characteristic, complemented, Sylow
26	Q₆₄	—	146	1	no	—
27	D₃₂	—	146	1	no	—
28	C₆₄	C₂×D₇₃	1	1	yes	characteristic
29	Q₃₂	—	292	1	no	—
30	D₁₆	—	292	1	no	—
31	C₃₂	D₂₉₂	1	1	yes	characteristic
32	Q₁₆	—	584	1	no	—
33	D₈	—	584	1	no	—
34	C₁₆	D₅₈₄	1	1	yes	characteristic
35	Q₈	—	1168	1	no	—
36	D₄	—	1168	1	no	—
37	C₈	D₁₁₆₈	1	1	yes	characteristic
38	C₂²	—	2336	1	no	—
39	C₄	—	2336	1	no	—
40	C₄	D₂₃₃₆	1	1	yes	characteristic
41	C₂	—	4672	1	no	—
42	C₂	D₄₆₇₂	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.