Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C2×#124×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#124 | D59 |
| hypocenter | C59 | #2326 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×Dic59 | C2 | semidirect |
| 3. #16837309 | C2 | semidirect |
| 5. #16837295 | C2 | semidirect |
| 6. #16837277 | C2 | semidirect |
| 7. #16837272 | C2 | semidirect |
| 8. #16837248 | C2 | semidirect |
| 27. #124×C59 | C4 | semidirect |
| 33. C2×Q8×C59 | C2×C4 | semidirect |
| 47. C22⋊C4×C59 | C2×C4 | semidirect |
| 48. C42×C59 | C2×C4 | semidirect |
| 121. C59 | #2326 | semidirect |
| 125. #124 | Dic59 | semidirect |
| 145. C2×Q8 | C2×Dic59 | semidirect |
| 165. C22⋊C4 | C2×Dic59 | semidirect |
| 169. C42 | C2×Dic59 | semidirect |