Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1536 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1536 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C2×2−1+4×C59 | C2 |
| hypercenter | C2×2−1+4 | D59 |
| hypocenter | C59 | #3487 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11745689 | C2 | semidirect |
| 2. #16838071 | C2 | semidirect |
| 3. #16838063 | C2 | semidirect |
| 4. #16837966 | C2 | semidirect |
| 5. #16837909 | C2 | semidirect |
| 6. #16837880 | C2 | semidirect |
| 7. C2×2−1+4×C59 | C2 | semidirect |
| 12. #14273723 | C22 | semidirect |
| 13. #14273716 | C22 | semidirect |
| 15. #14273703 | C22 | semidirect |
| 16. #14273701 | C22 | semidirect |
| 17. #14273698 | C22 | semidirect |
| 19. Q8×Dic59 | C22 | semidirect |
| 20. C4×C22⋊D59 | C22 | semidirect |
| 24. C2×#41×C59 | C22 | semidirect |
| 26. C22×Q8×C59 | C22 | semidirect |
| 31. C2×Q8×C59 | D4 | semidirect |
| 88. C2×2−1+4 | D59 | semidirect |
| 95. C59 | #3487 | semidirect |
| 100. C2×#41 | C2×D59 | semidirect |
| 102. C22×Q8 | C2×D59 | semidirect |
| 120. C2×Q8 | C22⋊D59 | semidirect |