Subgroups — C₃×#322 #4569

Order 192.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₈	C₂	1	2	yes	maximal
2	C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#322	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₈	C₄	1	4	yes	—
5	C₂×C₃×C₈	C₄	1	2	yes	—
6	C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₄×C₈	C₂×C₃	1	2	yes	—
8	C₄×C₈	C₂×C₃	1	1	yes	characteristic
9	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
11	C₃×C₈	—	2	4	no	—
12	C₃×C₈	C₈	1	4	yes	complemented
13	C₂×C₈	C₃×C₄	1	4	yes	—
14	C₂×C₈	C₃×C₄	1	2	yes	—
15	C₄²	C₂²×C₃	1	1	yes	characteristic
16	C₂²×C₃	C₄²	1	1	yes	characteristic
17	C₃×C₄	C₂×C₈	1	2	yes	—
18	C₃×C₄	M₁₆	1	4	yes	—
19	C₂×C₄	C₂×C₃×C₄	1	1	yes	characteristic
20	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
21	C₈	—	2	4	no	—
22	C₈	C₃×C₈	1	4	yes	complemented
23	C₂×C₃	C₄×C₈	1	1	yes	characteristic
24	C₂×C₃	#97	1	2	yes	—
25	C₂²	C₃×C₄²	1	1	yes	characteristic
26	C₄	C₂×C₃×C₈	1	2	yes	—
27	C₄	C₃×M₁₆	1	4	yes	—
28	C₃	#322	1	1	yes	characteristic, direct product factor, Sylow
29	C₂	C₃×C₄×C₈	1	1	yes	characteristic
30	C₂	C₃×#97	1	2	yes	—

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.

subgroup	index
C₃×C₄×C₈	2
#322	3