Subgroups — #4466

Order 192.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#97	C₂	1	1	yes	maximal, characteristic
2	#812	C₂	1	2	yes	maximal
3	#347	—	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	M₃₂	—	3	2	no	—
9	#97	D₃	1	1	yes	characteristic
10	C₂×C₃×C₄	—	2	1	no	—
11	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₃×C₈	—	2	1	no	—
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	M₁₆	1	1	yes	characteristic
19	C₃×C₄	—	4	1	no	—
20	C₃×C₄	C₄²	1	1	yes	characteristic
21	C₃×C₄	M₁₆	1	1	yes	characteristic
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	C₂×Dic₃	1	1	yes	characteristic
24	C₈	—	2	1	no	—
25	C₈	C₄×D₃	1	2	yes	—
26	C₂×C₃	—	2	1	no	—
27	C₂×C₃	#97	1	1	yes	characteristic
28	C₂²	#208	1	1	yes	characteristic
29	C₄	—	4	1	no	—
30	C₄	#208	1	1	yes	characteristic
31	C₄	C₄×Dic₃	1	1	yes	characteristic
32	C₃	#347	1	1	yes	characteristic, complemented, Sylow
33	C₂	—	2	1	no	—
34	C₂	#803	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₃⋊C₁₆	C₄	semidirect
32. C₃	#347	semidirect

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