Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
1056 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1056 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, socle | C23×C71 | C24 |
| Fitting | C22×C22⋊C4×C71 | C2 |
| hypercenter | C22×C22⋊C4 | D71 |
| hypocenter | C71 | #2404 |
| LCS | G ▷ C23×C71 ▷ C71 | |
| UCS | C1 ◁ C23 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11765865 | C2 | semidirect |
| 2. C2×#14556097 | C2 | semidirect |
| 3. #17985911 | C2 | semidirect |
| 4. #17985908 | C2 | semidirect |
| 5. #17985878 | C2 | semidirect |
| 6. #17985875 | C2 | semidirect |
| 7. #17985862 | C2 | semidirect |
| 8. C22×C22⋊C4×C71 | C2 | semidirect |
| 11. C22×Dic142 | C22 | semidirect |
| 12. C22×D284 | C22 | semidirect |
| 15. C22×C4×D71 | C22 | semidirect |
| 19. C2×(C2×D71)⋊C4 | C22 | semidirect |
| 20. C71⋊#95 | C22 | semidirect |
| 21. C71⋊#95 | C22 | semidirect |
| 22. C71⋊#95 | C22 | semidirect |
| 40. C2×C22⋊D71 | D4 | semidirect |
| 58. C22×C4×C71 | D4 | semidirect |
| 76. C23×C71 | #41 | semidirect |
| 134. C71 | #2404 | semidirect |
| 137. C22×C22⋊C4 | D71 | semidirect |
| 189. C22×C4 | C22⋊D71 | semidirect |
| 215. C23 | #11765865 | semidirect |