Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
598 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 133 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×#398 | C2 |
| hypercenter | #398 | D59 |
| hypocenter | C59 | #2661 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #398 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273712 | C2 | semidirect |
| 2. C2×#14273702 | C2 | semidirect |
| 3. #16837328 | C2 | semidirect |
| 4. #16837319 | C2 | semidirect |
| 5. #16837319 | C2 | semidirect |
| 6. #16837312 | C2 | semidirect |
| 7. #16837312 | C2 | semidirect |
| 8. #16837303 | C2 | semidirect |
| 9. #16837291 | C2 | semidirect |
| 10. #16837249 | C2 | semidirect |
| 11. C59×#398 | C2 | semidirect |
| 59. C2×C4×D59 | D4 | semidirect |
| 158. #398 | D59 | semidirect |
| 167. C59 | #2661 | semidirect |