Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
796 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 796 conjugacy classes of subgroups — too many to draw. Only its 141 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 | #2670 |
| 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×#14273697 | C2 | semidirect |
| 3. #16837320 | C2 | semidirect |
| 4. #16837312 | C2 | semidirect |
| 5. #16837311 | C2 | semidirect |
| 6. #16837302 | C2 | semidirect |
| 7. #16837291 | C2 | semidirect |
| 8. #16837257 | C2 | semidirect |
| 9. C59×#393 | C2 | semidirect |
| 13. C22×D236 | C22 | semidirect |
| 17. C2×Dic59⋊C4 | C22 | semidirect |
| 23. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 24. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 25. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 26. C2×C4×Dic59 | C22 | semidirect |
| 27. C59⋊#95 | C22 | semidirect |
| 28. C22×Q8×C59 | C22 | semidirect |
| 31. #95×C59 | C22 | semidirect |
| 32. #95×C59 | C22 | semidirect |
| 69. (C2×D59)⋊C4 | D4 | semidirect |
| 161. #393 | D59 | semidirect |
| 167. C59 | #2670 | semidirect |
| 169. C22×Q8 | C2×D59 | semidirect |
| 189. #95 | C2×D59 | semidirect |
| 190. #95 | C2×D59 | semidirect |