Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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×#394 | C2 |
| hypercenter | #394 | D59 |
| hypocenter | C59 | #2388 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#11745687 | C2 | semidirect |
| 2. C2×#14273689 | C2 | semidirect |
| 3. C2×(C22⋊D59)⋊C4 | C2 | semidirect |
| 4. #16837322 | C2 | semidirect |
| 5. #16837317 | C2 | semidirect |
| 6. #16837315 | C2 | semidirect |
| 7. #16837311 | C2 | semidirect |
| 8. #16837310 | C2 | semidirect |
| 9. C22⋊C4×Dic59 | C2 | semidirect |
| 10. #16837249 | C2 | semidirect |
| 11. C59×#394 | C2 | semidirect |
| 56. C22×Dic59 | D4 | semidirect |
| 68. C2×C4×D59 | D4 | semidirect |
| 99. C22×D59 | #41 | semidirect |
| 110. C2×C4×C59 | #41 | semidirect |
| 123. C2×Dic59 | #41 | semidirect |
| 172. #394 | D59 | semidirect |
| 178. C59 | #2388 | semidirect |
| 294. C2×C4 | #11745687 | semidirect |