Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2793 conjugacy classes of subgroups; only the 428 normal subgroups are shown.
This group has 2793 conjugacy classes of subgroups — too many to draw. Only its 428 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C2×C32×C42 | C22 |
| hypercenter | C2×C42 | D32 |
| hypocenter | C32 | #2867 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64083 | C2 | semidirect |
| 2. C2×C3×#874 | C2 | semidirect |
| 3. C2×#63911 | C2 | semidirect |
| 4. C3×C42×Dic3 | C2 | semidirect |
| 21. C2×#874 | D3 | semidirect |
| 23. C42×Dic3 | D3 | semidirect |
| 33. C32×C42 | D4 | semidirect |
| 34. C3×C4×Dic3 | D4 | semidirect |
| 94. C3×C42 | D12 | semidirect |
| 95. C3×C42 | #67 | semidirect |
| 96. C4×Dic3 | D12 | semidirect |
| 103. C32×C4 | #127 | semidirect |
| 104. C3×Dic3 | #127 | semidirect |
| 155. C42 | #626 | semidirect |
| 174. C3×C4 | #874 | semidirect |
| 175. C3×C4 | #940 | semidirect |
| 176. Dic3 | #874 | semidirect |
| 177. C32 | #2867 | semidirect |
| 207. C4 | #63911 | semidirect |
| 209. C3 | #73318 | semidirect |
| 210. C3 | #83185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64083 | 2 |
| C2×C3×#874 | 2 |
| C2×#63911 | 2 |
| C3×C42×Dic3 | 2 |
| #83185 | 3 |
| #73318 | 3 |