Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D284 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #436×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #436 | D71 |
| hypocenter | C71 | #3353 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986719 | C2 | semidirect |
| 3. #17986404 | C2 | semidirect |
| 4. #17986335 | C2 | semidirect |
| 5. #17986324 | C2 | semidirect |
| 6. #17986285 | C2 | semidirect |
| 7. #17986280 | C2 | semidirect |
| 8. #17986245 | C2 | semidirect |
| 9. C4×#11765854 | C2 | semidirect |
| 10. #17986041 | C2 | semidirect |
| 11. #436×C71 | C2 | semidirect |
| 99. C8×C71 | #41 | semidirect |
| 123. C71 | #3353 | semidirect |
| 133. #436 | D71 | semidirect |
| 222. C8 | #11765864 | semidirect |