Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 | C22×C71 | C23×C4 |
| Fitting | #384×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #384 | D71 |
| hypocenter | C71 | #2326 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14556093 | C2 | semidirect |
| 4. #17985904 | C2 | semidirect |
| 6. #17985889 | C2 | semidirect |
| 7. #17985870 | C2 | semidirect |
| 8. #17985845 | C2 | semidirect |
| 9. #384×C71 | C2 | semidirect |
| 13. #14556116 | C4 | semidirect |
| 33. C2×Dic142 | C2×C4 | semidirect |
| 46. (C2×D71)⋊C4 | C2×C4 | semidirect |
| 57. C42×C71 | C2×C4 | semidirect |
| 112. C71 | #2326 | semidirect |
| 120. #384 | D71 | semidirect |
| 169. C42 | C4×D71 | semidirect |