Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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 | C22×C59 | C23×C4 |
| Fitting | C59×#384 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #384 | D59 |
| hypocenter | C59 | #2326 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273692 | C2 | semidirect |
| 4. #16837307 | C2 | semidirect |
| 6. #16837292 | C2 | semidirect |
| 7. #16837273 | C2 | semidirect |
| 8. #16837248 | C2 | semidirect |
| 9. C59×#384 | C2 | semidirect |
| 13. #14273715 | C4 | semidirect |
| 46. C2×Dic118 | C2×C4 | semidirect |
| 50. C42×C59 | C2×C4 | semidirect |
| 53. (C2×D59)⋊C4 | C2×C4 | semidirect |
| 119. #384 | D59 | semidirect |
| 121. C59 | #2326 | semidirect |
| 169. C42 | C4×D59 | semidirect |