Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
580 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 125 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 | #2819 |
| 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×#14273713 | C2 | semidirect |
| 3. #16837320 | C2 | semidirect |
| 4. #16837317 | C2 | semidirect |
| 5. #16837315 | C2 | semidirect |
| 6. #16837313 | C2 | semidirect |
| 7. #16837312 | C2 | semidirect |
| 8. #16837311 | C2 | semidirect |
| 9. #16837311 | C2 | semidirect |
| 10. #16837266 | C2 | semidirect |
| 11. C59×#393 | C2 | semidirect |
| 73. C4×Dic59 | D4 | semidirect |
| 163. #393 | D59 | semidirect |
| 168. C59 | #2819 | semidirect |