Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
438 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63970 |
| commutator, cosocle | C32×C42 | C23 |
| Frattini | C42 | C2×D32 |
| Fitting | C32×#127 | C22 |
| socle | C22×C32 | #121 |
| hypercenter | #127 | D32 |
| hypocenter | C32 | #1687 |
| LCS | G ▷ C32×C42 ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#5073 | C2 | semidirect |
| 2. C3×#5072 | C2 | semidirect |
| 3. #10590347 | C2 | semidirect |
| 4. #10590337 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589097 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 27. #5073 | D3 | semidirect |
| 29. #5072 | D3 | semidirect |
| 120. C3×C3⋊C8 | D8 | semidirect |
| 269. C3⋊C8 | #213 | semidirect |
| 338. C32 | #1687 | semidirect |
| 398. C3 | #71009 | semidirect |
| 399. C3 | #71283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5073 | 2 |
| C3×#5072 | 2 |
| #10590347 | 2 |
| #10590337 | 2 |
| #10589410 | 2 |
| #10589097 | 2 |
| #10589090 | 2 |
| #71283 | 3 |
| #71009 | 3 |