Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D113 |
| commutator, socle | C22×C113 | C24 |
| Fitting | #120×C113 | C2 |
| hypercenter | #120 | D113 |
| hypocenter | C113 | #560 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813618 | C2 | semidirect |
| 2. #16813615 | C2 | semidirect |
| 3. #16813604 | C2 | semidirect |
| 4. #16813603 | C2 | semidirect |
| 5. #16813595 | C2 | semidirect |
| 6. #16813594 | C2 | semidirect |
| 7. #16813593 | C2 | semidirect |
| 8. #16813591 | C2 | semidirect |
| 9. #120×C113 | C2 | semidirect |
| 10. C2×D452 | C22 | semidirect |
| 14. C2×C22⋊D113 | C22 | semidirect |
| 15. C22×Dic113 | C22 | semidirect |
| 16. C2×C4×D113 | C22 | semidirect |
| 17. C4⋊Dic113 | C22 | semidirect |
| 18. #14268626 | C22 | semidirect |
| 19. #14268626 | C22 | semidirect |
| 23. C22⋊Dic113 | C22 | semidirect |
| 24. #14268624 | C22 | semidirect |
| 25. C4×Dic113 | C22 | semidirect |
| 74. C113 | #560 | semidirect |
| 84. #120 | D113 | semidirect |