Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
628 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 131 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×#393 | C2 |
| hypercenter | #393 | D59 |
| hypocenter | C59 | #2631 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #393 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273716 | C2 | semidirect |
| 2. C2×(C22⋊D59)⋊C4 | C2 | semidirect |
| 3. #16837331 | C2 | semidirect |
| 4. #16837313 | C2 | semidirect |
| 5. #16837312 | C2 | semidirect |
| 6. #16837311 | C2 | semidirect |
| 7. #16837311 | C2 | semidirect |
| 8. #16837280 | C2 | semidirect |
| 9. #16837279 | C2 | semidirect |
| 10. #16837269 | C2 | semidirect |
| 11. C59×#393 | C2 | semidirect |
| 74. C4×Dic59 | D4 | semidirect |
| 163. #393 | D59 | semidirect |
| 170. C59 | #2631 | semidirect |