Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#496 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #496 | D59 |
| hypocenter | C59 | #3153 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273756 | C2 | semidirect |
| 2. C2×#14273751 | C2 | semidirect |
| 3. #16837950 | C2 | semidirect |
| 4. #124×D59 | C2 | semidirect |
| 5. #16837797 | C2 | semidirect |
| 6. #16837796 | C2 | semidirect |
| 7. #16837789 | C2 | semidirect |
| 8. #16837785 | C2 | semidirect |
| 9. #16837783 | C2 | semidirect |
| 10. #16837354 | C2 | semidirect |
| 11. C59×#496 | C2 | semidirect |
| 17. C2×Dic236 | C22 | semidirect |
| 18. C2×#11745672 | C22 | semidirect |
| 21. C2×#11745670 | C22 | semidirect |
| 24. #14273727 | C22 | semidirect |
| 28. #14273714 | C22 | semidirect |
| 34. #14273638 | C22 | semidirect |
| 35. C8×Dic59 | C22 | semidirect |
| 36. C2×SD16×C59 | C22 | semidirect |
| 38. #127×C59 | C22 | semidirect |
| 40. #97×C59 | C22 | semidirect |
| 79. #11745659 | D4 | semidirect |
| 142. #496 | D59 | semidirect |
| 146. C59 | #3153 | semidirect |
| 157. C2×SD16 | C2×D59 | semidirect |
| 162. #127 | C2×D59 | semidirect |
| 174. #97 | C2×D59 | semidirect |