Subgroups — #4461

Order 192.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊C₁₆	C₂	1	2	yes	maximal
3	#346	—	3	1	no	maximal, Sylow
4	C₂×C₃×C₈	C₄	1	1	yes	characteristic
5	C₂×C₃×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄²	C₄	1	1	yes	characteristic
7	C₃⋊C₁₆	C₄	1	4	yes	complemented
8	C₂×C₁₆	—	3	2	no	—
9	C₄×C₈	D₃	1	1	yes	characteristic
10	C₂×C₃×C₄	C₈	1	2	yes	—
11	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	C₈	1	2	yes	—
13	C₃×C₈	C₂×C₄	1	2	yes	—
14	C₂×C₈	Dic₃	1	1	yes	characteristic
15	C₂×C₈	C₂×D₃	1	1	yes	characteristic
16	C₄²	Dic₃	1	1	yes	characteristic
17	C₁₆	—	3	4	no	—
18	C₂²×C₃	C₂×C₈	1	1	yes	characteristic
19	C₃×C₄	—	2	2	no	—
20	C₃×C₄	C₄²	1	1	yes	characteristic
21	C₃×C₄	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄	C₃⋊C₈	1	2	yes	—
23	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
24	C₈	C₃⋊C₈	1	2	yes	—
25	C₈	C₄×D₃	1	2	yes	—
26	C₂×C₃	C₄×C₈	1	1	yes	characteristic
27	C₂×C₃	M₃₂	1	2	yes	—
28	C₂²	C₂×C₃⋊C₈	1	1	yes	characteristic
29	C₄	—	2	2	no	—
30	C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
31	C₄	C₄×Dic₃	1	1	yes	characteristic
32	C₃	#346	1	1	yes	characteristic, complemented, Sylow
33	C₂	C₄×C₃⋊C₈	1	1	yes	characteristic
34	C₂	#812	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. C₃⋊C₁₆	C₄	semidirect
32. C₃	#346	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.