Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #407×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #407 | D71 |
| hypocenter | C71 | #3004 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ #407 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic142 | C2 | semidirect |
| 2. C2×#14556161 | C2 | semidirect |
| 4. #17986157 | C2 | semidirect |
| 5. #17986140 | C2 | semidirect |
| 6. #17986009 | C2 | semidirect |
| 7. #407×C71 | C2 | semidirect |
| 16. C2×Dic284 | C22 | semidirect |
| 17. C2×#11765854 | C22 | semidirect |
| 24. #14556053 | C22 | semidirect |
| 35. C2×Dic142 | D4 | semidirect |
| 93. C22×C71 | #137 | semidirect |
| 109. C71 | #3004 | semidirect |
| 116. #407 | D71 | semidirect |
| 204. C22 | #14556161 | semidirect |