Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
604 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 141 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×#383 | C2 |
| hypercenter | #383 | D59 |
| hypocenter | C59 | #2598 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×D236 | C2 | semidirect |
| 2. C2×#14273684 | C2 | semidirect |
| 3. #16837342 | C2 | semidirect |
| 4. #16837339 | C2 | semidirect |
| 5. #16837320 | C2 | semidirect |
| 7. #16837294 | C2 | semidirect |
| 8. #16837280 | C2 | semidirect |
| 9. #16837280 | C2 | semidirect |
| 10. #16837276 | C2 | semidirect |
| 11. C59×#383 | C2 | semidirect |
| 59. C42×C59 | D4 | semidirect |
| 156. #383 | D59 | semidirect |
| 157. C59 | #2598 | semidirect |
| 217. C42 | D236 | semidirect |