Subgroups — C₃×#383 #5257

Order 192.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₃×#95	C₂	1	6	yes	maximal
3	#383	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₄	C₂²	1	4	yes	—
5	C₂²×C₃×C₄	C₂²	1	3	yes	—
6	C₃×C₄²	C₄	1	4	yes	complemented
7	C₂×C₄²	C₂×C₃	1	1	yes	characteristic
8	#95	C₂×C₃	1	6	yes	—
9	C₂³×C₃	C₂³	1	1	yes	characteristic
10	C₂×C₃×C₄	—	2	6	no	—
11	C₂×C₃×C₄	—	2	12	no	—
12	C₂×C₃×C₄	C₂×C₄	1	6	yes	—
13	C₂²×C₄	C₂²×C₃	1	4	yes	—
14	C₂²×C₄	C₂²×C₃	1	3	yes	—
15	C₄²	C₃×C₄	1	4	yes	complemented
16	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₃	#41	1	6	yes	—
18	C₃×C₄	—	2	6	no	—
19	C₃×C₄	—	4	4	no	—
20	C₂³	C₂³×C₃	1	1	yes	characteristic
21	C₂×C₄	—	2	6	no	—
22	C₂×C₄	—	2	12	no	—
23	C₂×C₄	C₂×C₃×C₄	1	6	yes	—
24	C₂×C₃	#117	1	3	yes	—
25	C₂×C₃	#126	1	4	yes	—
26	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
27	C₂²	C₃×#41	1	6	yes	—
28	C₄	—	2	6	no	—
29	C₄	—	4	4	no	—
30	C₃	#383	1	1	yes	characteristic, direct product factor, Sylow
31	C₂	C₃×#117	1	3	yes	—
32	C₂	C₃×#126	1	4	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.