Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
492 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 135 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×#397 | C2 |
| hypercenter | #397 | D59 |
| hypocenter | C59 | #2599 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #397 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273692 | C2 | semidirect |
| 3. #16837333 | C2 | semidirect |
| 4. #16837323 | C2 | semidirect |
| 7. #16837285 | C2 | semidirect |
| 8. #16837284 | C2 | semidirect |
| 10. #16837269 | C2 | semidirect |
| 138. C59 | #2599 | semidirect |