Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #431×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #431 | D71 |
| hypocenter | C71 | #3208 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #17986556 | C2 | semidirect |
| 3. #17986372 | C2 | semidirect |
| 4. #17986346 | C2 | semidirect |
| 5. #17986200 | C2 | semidirect |
| 6. #17986152 | C2 | semidirect |
| 7. #431×C71 | C2 | semidirect |
| 11. C2×#11765854 | C22 | semidirect |
| 12. #14556128 | C22 | semidirect |
| 13. #14556128 | C22 | semidirect |
| 22. C4×Dic142 | C22 | semidirect |
| 24. #14556050 | C22 | semidirect |
| 26. C4⋊C8×C71 | C22 | semidirect |
| 28. C4×C8×C71 | C22 | semidirect |
| 65. C2×C4×C71 | SD16 | semidirect |
| 105. C71 | #3208 | semidirect |
| 112. #431 | D71 | semidirect |
| 130. C4⋊C8 | C2×D71 | semidirect |
| 133. C4×C8 | C2×D71 | semidirect |
| 180. C2×C4 | #11765854 | semidirect |