Subgroups — C₂×#22604432 #32914764

Order 18464.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22604432	C₂	1	2	yes	maximal, direct product factor
2	C₂×#17987239	C₂	1	1	yes	maximal, characteristic
3	#17987239	C₄	1	1	yes	characteristic
4	#17987239	C₂²	1	1	yes	characteristic
5	C₂×#14556313	C₄	1	1	yes	characteristic
6	C₂×D₅₇₇	C₈	1	1	yes	characteristic
7	#14556313	C₈	1	1	yes	characteristic
8	#14556313	C₂×C₄	1	1	yes	characteristic
9	C₂×C₅₇₇	C₁₆	1	1	yes	characteristic, complemented
10	D₅₇₇	C₁₆	1	1	yes	characteristic, complemented
11	D₅₇₇	C₂×C₈	1	1	yes	characteristic
12	C₅₇₇	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₆	—	577	1	no	maximal, Sylow
14	C₂×C₈	—	577	1	no	—
15	C₁₆	—	577	2	no	—
16	C₂×C₄	—	577	1	no	—
17	C₈	—	577	1	no	—
18	C₈	—	577	1	no	—
19	C₂²	—	577	1	no	—
20	C₄	—	577	1	no	—
21	C₄	—	577	1	no	—
22	C₂	—	577	1	no	—
23	C₂	—	577	1	no	—
24	C₂	#22604432	1	1	yes	characteristic, direct product factor

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.