Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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×#383 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #383 | D59 |
| hypocenter | C59 | #2337 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #16837306 | C2 | semidirect |
| 3. #16837294 | C2 | semidirect |
| 4. #16837291 | C2 | semidirect |
| 6. #16837276 | C2 | semidirect |
| 7. C4×C4⋊Dic59 | C2 | semidirect |
| 8. #16837249 | C2 | semidirect |
| 9. C59×#383 | C2 | semidirect |
| 13. #14273715 | C4 | semidirect |
| 47. C2×Dic118 | C2×C4 | semidirect |
| 48. C42×C59 | C2×C4 | semidirect |
| 52. (C2×D59)⋊C4 | C2×C4 | semidirect |
| 53. (C2×D59)⋊C4 | C2×C4 | semidirect |
| 125. #383 | D59 | semidirect |
| 128. C59 | #2337 | semidirect |
| 177. C42 | C4×D59 | semidirect |