Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1212 conjugacy classes of subgroups; only the 509 normal subgroups are shown.
This group has 1212 conjugacy classes of subgroups — too many to draw. Only its 509 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C22×C42×C59 | C2 |
| hypercenter | C22×C42 | D59 |
| hypocenter | C59 | #3444 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C42 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837959 | C2 | semidirect |
| 2. #16837952 | C2 | semidirect |
| 3. #16837936 | C2 | semidirect |
| 4. #16837913 | C2 | semidirect |
| 5. C4×#11745685 | C2 | semidirect |
| 6. C22×C42×C59 | C2 | semidirect |
| 8. #14273727 | C22 | semidirect |
| 9. #14273724 | C22 | semidirect |
| 10. #14273721 | C22 | semidirect |
| 11. #14273719 | C22 | semidirect |
| 12. #14273715 | C22 | semidirect |
| 17. C4×Dic118 | C22 | semidirect |
| 18. C4×D236 | C22 | semidirect |
| 21. #14273684 | C22 | semidirect |
| 22. C42×D59 | C22 | semidirect |
| 55. C2×C4×C59 | #41 | semidirect |
| 82. C22×C42 | D59 | semidirect |
| 83. C59 | #3444 | semidirect |
| 137. C2×C4 | #11745685 | semidirect |