Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C71 | C23×C4 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #405×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #405 | D71 |
| hypocenter | C71 | #2949 |
| LCS | G ▷ C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17986476 | C2 | semidirect |
| 4. #17986101 | C2 | semidirect |
| 5. C4×#11765854 | C2 | semidirect |
| 6. #17986037 | C2 | semidirect |
| 7. #17986009 | C2 | semidirect |
| 9. #405×C71 | C2 | semidirect |
| 12. C2×#11765854 | C4 | semidirect |
| 15. C4×Dic142 | C22 | semidirect |
| 23. #14556062 | C22 | semidirect |
| 24. #14556060 | C22 | semidirect |
| 25. #14556053 | C22 | semidirect |
| 30. #97×C71 | C22 | semidirect |
| 31. C4×C8×C71 | C22 | semidirect |
| 35. C2×Dic142 | C2×C4 | semidirect |
| 43. #11765854 | C2×C4 | semidirect |
| 44. #11765854 | C2×C4 | semidirect |
| 56. C2×C8×C71 | C2×C4 | semidirect |
| 104. C71 | #2949 | semidirect |
| 113. #405 | D71 | semidirect |
| 134. #97 | C2×D71 | semidirect |
| 135. C4×C8 | C2×D71 | semidirect |
| 151. C2×C8 | C4×D71 | semidirect |