Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
543 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63979 |
| commutator, cosocle | C32×C42 | C23 |
| Frattini | C42 | C2×D32 |
| Fitting | C32×#127 | C22 |
| socle | C22×C32 | #127 |
| hypercenter | #127 | D32 |
| hypocenter | C32 | #1721 |
| 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. #10592769 | C2 | semidirect |
| 2. C3×#5073 | C2 | semidirect |
| 3. C3×#5073 | C2 | semidirect |
| 4. #10590369 | C2 | semidirect |
| 5. #10590352 | C2 | semidirect |
| 6. #10590273 | C2 | semidirect |
| 7. #10589078 | C2 | semidirect |
| 28. #5073 | D3 | semidirect |
| 29. #5073 | D3 | semidirect |
| 108. C3×C3⋊C8 | D8 | semidirect |
| 240. C3⋊C8 | #213 | semidirect |
| 303. C32 | #1721 | semidirect |
| 355. C3 | #71279 | semidirect |
| 356. C3 | #71280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592769 | 2 |
| C3×#5073 | 2 |
| #10590369 | 2 |
| #10590352 | 2 |
| #10590273 | 2 |
| #10589078 | 2 |
| #71280 | 3 |
| #71279 | 3 |