Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×C22⋊D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | D42×C59 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | D42 | D59 |
| hypocenter | C59 | #3294 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838056 | C2 | semidirect |
| 2. #16837748 | C2 | semidirect |
| 3. #16837713 | C2 | semidirect |
| 4. #16837682 | C2 | semidirect |
| 5. #16837636 | C2 | semidirect |
| 6. #16837594 | C2 | semidirect |
| 7. #16837536 | C2 | semidirect |
| 8. C4×#11745669 | C2 | semidirect |
| 9. D4×C59⋊C8 | C2 | semidirect |
| 10. C2×#14273648 | C2 | semidirect |
| 11. D42×C59 | C2 | semidirect |
| 14. C2×#11745669 | C22 | semidirect |
| 15. C22×C59⋊C8 | C22 | semidirect |
| 16. #14273727 | C22 | semidirect |
| 19. #14273701 | C22 | semidirect |
| 20. C4×D236 | C22 | semidirect |
| 21. C2×C4⋊Dic59 | C22 | semidirect |
| 22. #14273660 | C22 | semidirect |
| 23. #14273660 | C22 | semidirect |
| 24. C4⋊(C59⋊C8) | C22 | semidirect |
| 27. #14273648 | C22 | semidirect |
| 28. #14273648 | C22 | semidirect |
| 29. #14273648 | C22 | semidirect |
| 30. #14273647 | C22 | semidirect |
| 31. C22⋊(C59⋊C8) | C22 | semidirect |
| 32. C4×C59⋊C8 | C22 | semidirect |
| 92. D4×C59 | D8 | semidirect |
| 93. D4×C59 | #41 | semidirect |
| 144. D42 | D59 | semidirect |
| 154. C59 | #3294 | semidirect |
| 239. D4 | #11745669 | semidirect |
| 240. D4 | #11745687 | semidirect |