Subgroups — C₂×#3708 #63772

Order 288.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	#3708	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
4	C₃⋊(C₃⋊C₈)	C₄	1	1	yes	characteristic
5	C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
6	C₂×C₃⋊C₈	—	6	2	no	—
7	C₂²×C₃²	C₈	1	1	yes	characteristic
8	C₃²×C₄	C₈	1	1	yes	characteristic
9	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₆	—	9	1	no	maximal, Sylow
11	C₂×C₃×C₄	—	2	2	no	—
12	C₃⋊C₈	—	6	2	no	—
13	C₃⋊C₈	—	6	2	no	—
14	C₂×C₃²	C₁₆	1	2	yes	complemented
15	C₂×C₃²	C₂×C₈	1	1	yes	characteristic
16	C₂×C₈	—	9	1	no	—
17	C₁₆	—	9	2	no	—
18	C₂²×C₃	—	2	2	no	—
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	—	2	2	no	—
21	C₃²	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₄	#157	1	1	yes	characteristic
23	C₈	—	9	1	no	—
24	C₈	—	9	1	no	—
25	C₂×C₃	—	2	4	no	—
26	C₂×C₃	—	2	2	no	—
27	C₂²	#622	1	1	yes	characteristic
28	C₄	#622	1	1	yes	characteristic
29	C₄	C₂×#157	1	1	yes	characteristic
30	C₃	—	2	2	no	—
31	C₂	#3708	1	2	yes	direct product factor
32	C₂	C₂×#622	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.