Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 181 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×#379 | C2 |
| hypercenter | #379 | D59 |
| hypocenter | C59 | #2405 |
| LCS | G ▷ C23×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14273711 | C2 | semidirect |
| 3. C22×C22⋊Dic59 | C2 | semidirect |
| 4. #16837318 | C2 | semidirect |
| 5. #16837279 | C2 | semidirect |
| 6. #16837277 | C2 | semidirect |
| 7. #16837257 | C2 | semidirect |
| 8. C59×#379 | C2 | semidirect |
| 15. C23×Dic59 | C22 | semidirect |
| 16. C23×Dic59 | C22 | semidirect |
| 18. C2×C4⋊Dic59 | C22 | semidirect |
| 21. C2×C22⋊Dic59 | C22 | semidirect |
| 22. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 23. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 24. C59⋊#95 | C22 | semidirect |
| 27. C2×C22⋊C4×C59 | C22 | semidirect |
| 28. C2×C22⋊C4×C59 | C22 | semidirect |
| 119. C22×C59 | #123 | semidirect |
| 150. #379 | D59 | semidirect |
| 151. C59 | #2405 | semidirect |
| 169. C2×C22⋊C4 | C2×D59 | semidirect |
| 170. C2×C22⋊C4 | C2×D59 | semidirect |
| 268. C22 | #14273711 | semidirect |