Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×#125×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#125 | D59 |
| hypocenter | C59 | C2×#540 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838008 | C2 | direct (N × H) |
| 2. C2×#14273724 | C2 | semidirect |
| 3. C2×#14273712 | C2 | semidirect |
| 4. C2×#14273702 | C2 | semidirect |
| 5. C2×#14273702 | C2 | semidirect |
| 6. C2×#14273689 | C2 | semidirect |
| 7. C2×#14273684 | C2 | semidirect |
| 8. C2×#125×C59 | C2 | semidirect |
| 14. #14273724 | C22 | semidirect |
| 15. #14273712 | C22 | semidirect |
| 16. #14273702 | C22 | semidirect |
| 17. #14273702 | C22 | semidirect |
| 18. #14273689 | C22 | semidirect |
| 19. #14273684 | C22 | semidirect |
| 25. #125×C59 | C22 | semidirect |
| 93. C2×C59 | #540 | semidirect |
| 100. C2×#125 | D59 | semidirect |
| 106. C59 | C2×#540 | semidirect |
| 113. #125 | C2×D59 | semidirect |
| 192. C2 | #16838008 | direct (N × H) |