Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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 | #381×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #381 | D71 |
| hypocenter | C71 | #2377 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #17985899 | C2 | semidirect |
| 3. #17985891 | C2 | semidirect |
| 4. #17985882 | C2 | semidirect |
| 5. #17985877 | C2 | semidirect |
| 6. #17985875 | C2 | semidirect |
| 7. #17985873 | C2 | semidirect |
| 8. #17985859 | C2 | semidirect |
| 9. #381×C71 | C2 | semidirect |
| 13. #14556102 | C4 | semidirect |
| 37. C2×C22⋊D71 | C2×C4 | semidirect |
| 45. C4⋊Dic71 | C2×C4 | semidirect |
| 52. (C2×D71)⋊C4 | C2×C4 | semidirect |
| 56. C22×C4×C71 | C2×C4 | semidirect |
| 130. C71 | #2377 | semidirect |
| 138. #381 | D71 | semidirect |
| 176. C22×C4 | C4×D71 | semidirect |