Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
440 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 440 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, Frattini | C23 | C23×D59 |
| commutator, socle | C23×C59 | C24 |
| Fitting | C59×#382 | C2 |
| hypercenter | #382 | D59 |
| hypocenter | C59 | #2513 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837331 | C2 | semidirect |
| 2. #16837329 | C2 | semidirect |
| 6. #16837301 | C2 | semidirect |
| 7. #16837294 | C2 | semidirect |
| 8. #16837291 | C2 | semidirect |
| 9. C4⋊C4×Dic59 | C2 | semidirect |
| 10. C4×Dic59⋊C4 | C2 | semidirect |
| 11. C59×#382 | C2 | semidirect |
| 145. #382 | D59 | semidirect |
| 148. C59 | #2513 | semidirect |