Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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×#386 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #386 | D59 |
| hypocenter | C59 | #2376 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #16837299 | C2 | semidirect |
| 4. #16837296 | C2 | semidirect |
| 5. #16837290 | C2 | semidirect |
| 6. #16837284 | C2 | semidirect |
| 7. #16837275 | C2 | semidirect |
| 8. #16837260 | C2 | semidirect |
| 11. #14273708 | C4 | semidirect |
| 44. C22×Dic59 | C2×C4 | semidirect |
| 54. C22⋊Dic59 | C2×C4 | semidirect |
| 59. Dic59⋊C4 | C2×C4 | semidirect |
| 136. C59 | #2376 | semidirect |