Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
604 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D71 |
| commutator, socle | C23×C71 | C24 |
| Fitting | #392×C71 | C2 |
| hypercenter | #392 | D71 |
| hypocenter | C71 | #2598 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×Dic71 | C2 | semidirect |
| 2. C2×#14556084 | C2 | semidirect |
| 3. #17985939 | C2 | semidirect |
| 4. #17985935 | C2 | semidirect |
| 5. #17985913 | C2 | semidirect |
| 6. #17985893 | C2 | semidirect |
| 7. #17985879 | C2 | semidirect |
| 8. #17985879 | C2 | semidirect |
| 9. #17985871 | C2 | semidirect |
| 10. #17985866 | C2 | semidirect |
| 59. C4×Dic71 | D4 | semidirect |
| 146. C71 | #2598 | semidirect |