Finite Group DatabasebetaFinite Group DatabasebetaOrder 8768.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D137 |
| commutator, socle | C22×C137 | C24 |
| Fitting | #125×C137 | C2 |
| hypercenter | #125 | D137 |
| hypocenter | C137 | #554 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17984087 | C2 | semidirect |
| 2. #17984079 | C2 | semidirect |
| 3. #17984068 | C2 | semidirect |
| 4. #17984066 | C2 | semidirect |
| 5. #17984066 | C2 | semidirect |
| 6. C4×Dic274 | C2 | semidirect |
| 10. C4⋊C4×D137 | C2 | semidirect |
| 11. #125×C137 | C2 | semidirect |
| 38. D548 | Q8 | semidirect |
| 70. C137 | #554 | semidirect |
| 74. #125 | D137 | semidirect |