Finite Group DatabasebetaFinite Group DatabasebetaOrder 7232.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D113 |
| commutator | C4×C113 | C24 |
| Frattini | C4 | C23×D113 |
| Fitting | C2×D8×C113 | C2 |
| socle | C2×C113 | C22×D4 |
| hypercenter | C2×D8 | D113 |
| hypocenter | C113 | #576 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16813667 | C2 | semidirect |
| 2. #16813648 | C2 | semidirect |
| 3. #16813646 | C2 | semidirect |
| 4. #16813644 | C2 | semidirect |
| 5. #16813641 | C2 | semidirect |
| 6. D8×D113 | C2 | semidirect |
| 7. #16813628 | C2 | semidirect |
| 8. C2×D8×C113 | C2 | semidirect |
| 10. #14268647 | C22 | semidirect |
| 12. #14268646 | C22 | semidirect |
| 15. D4×D113 | C22 | semidirect |
| 16. Dic452 | C22 | semidirect |
| 17. #14268636 | C22 | semidirect |
| 18. #14268635 | C22 | semidirect |
| 19. D904 | C22 | semidirect |
| 20. #14268632 | C22 | semidirect |
| 21. #14268631 | C22 | semidirect |
| 22. #14268630 | C22 | semidirect |
| 23. C8×D113 | C22 | semidirect |
| 24. C2×D4×C113 | C22 | semidirect |
| 25. D8×C113 | C22 | semidirect |
| 26. D8×C113 | C22 | semidirect |
| 27. C2×C8×C113 | C22 | semidirect |
| 62. C113 | #576 | semidirect |
| 70. C2×D8 | D113 | semidirect |
| 79. C2×D4 | C2×D113 | semidirect |
| 85. D8 | C2×D113 | semidirect |
| 86. D8 | C2×D113 | semidirect |
| 90. C2×C8 | C2×D113 | semidirect |