Subgroups — C₃×#330 #4577

Order 192.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₃×#97	C₂	1	2	yes	maximal
3	#330	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	—	2	2	no	—
5	C₃×C₄⋊C₄	—	2	2	no	—
6	C₃×C₄⋊C₄	C₄	1	2	yes	—
7	C₃×C₄²	C₂²	1	1	yes	characteristic
8	#125	C₂×C₃	1	1	yes	characteristic
9	#97	C₂×C₃	1	2	yes	—
10	C₂×C₃×C₄	—	2	2	no	—
11	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₄	D₄	1	2	yes	—
13	C₃×C₈	—	2	4	no	—
14	C₂×C₈	—	2	2	no	—
15	C₄⋊C₄	—	2	2	no	—
16	C₄⋊C₄	C₃×C₄	1	2	yes	—
17	C₄²	C₂²×C₃	1	1	yes	characteristic
18	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₃×C₄	—	2	1	no	—
20	C₃×C₄	—	2	2	no	—
21	C₃×C₄	—	4	2	no	—
22	C₂×C₄	—	2	2	no	—
23	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
24	C₂×C₄	C₃×D₄	1	2	yes	—
25	C₈	—	2	4	no	—
26	C₂×C₃	#101	1	1	yes	characteristic
27	C₂×C₃	#104	1	2	yes	—
28	C₂²	C₃×C₂²⋊C₄	1	1	yes	characteristic
29	C₄	—	2	1	no	—
30	C₄	—	2	2	no	—
31	C₄	—	4	2	no	—
32	C₃	#330	1	1	yes	characteristic, direct product factor, Sylow
33	C₂	C₃×#101	1	1	yes	characteristic
34	C₂	C₃×#104	1	2	yes	—

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

N	H ≅ G/N	type
3. #330	C₃	direct (N × H)
32. C₃	#330	direct (N × H)

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