Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#405 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #405 | D59 |
| hypocenter | C59 | #3155 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273755 | C2 | semidirect |
| 2. C2×#14273749 | C2 | semidirect |
| 3. C22×D472 | C2 | semidirect |
| 4. #16837971 | C2 | semidirect |
| 5. #16837791 | C2 | semidirect |
| 6. #16837786 | C2 | semidirect |
| 7. #16837779 | C2 | semidirect |
| 8. C59×#405 | C2 | semidirect |
| 13. C2×Dic236 | C22 | semidirect |
| 14. C2×#11745660 | C22 | semidirect |
| 15. C2×#11745660 | C22 | semidirect |
| 19. C2×D472 | C22 | semidirect |
| 20. C2×D472 | C22 | semidirect |
| 21. #14273724 | C22 | semidirect |
| 22. #14273715 | C22 | semidirect |
| 28. #97×C59 | C22 | semidirect |
| 29. C4×C8×C59 | C22 | semidirect |
| 43. M16×C59 | D4 | semidirect |
| 44. C2×C8×C59 | D4 | semidirect |
| 109. #405 | D59 | semidirect |
| 110. C59 | #3155 | semidirect |
| 130. #97 | C2×D59 | semidirect |
| 131. C4×C8 | C2×D59 | semidirect |
| 152. M16 | D236 | semidirect |
| 153. C2×C8 | D236 | semidirect |