Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
477 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 477 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63909 |
| commutator, cosocle | C32×C42 | C23 |
| Frattini | C42 | C2×D32 |
| Fitting | C32×C4×C8 | C22 |
| socle | C22×C32 | #121 |
| hypercenter | C4×C8 | D32 |
| hypocenter | C32 | #1687 |
| LCS | G ▷ C32×C42 ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C4×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592394 | C2 | semidirect |
| 2. C3×#4688 | C2 | semidirect |
| 3. #10590349 | C2 | semidirect |
| 4. C3×#4457 | C2 | semidirect |
| 5. #10589091 | C2 | semidirect |
| 25. #4688 | D3 | semidirect |
| 29. #4457 | D3 | semidirect |
| 88. C32×C8 | D8 | semidirect |
| 202. C3×C8 | D24 | semidirect |
| 203. C3×C8 | #213 | semidirect |
| 259. C32 | #1687 | semidirect |
| 277. C8 | #3714 | semidirect |
| 305. C3 | #68540 | semidirect |
| 306. C3 | #70868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592394 | 2 |
| C3×#4688 | 2 |
| #10590349 | 2 |
| C3×#4457 | 2 |
| #10589091 | 2 |
| #70868 | 3 |
| #68540 | 3 |