Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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×#391 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #391 | D59 |
| hypocenter | C59 | C4×#124 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #391 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic59 | C2 | semidirect |
| 5. #16837294 | C2 | semidirect |
| 6. #16837267 | C2 | semidirect |
| 7. #16837249 | C2 | semidirect |
| 8. C42×Dic59 | C2 | semidirect |
| 9. C59×#391 | C2 | semidirect |
| 12. #14273716 | C4 | semidirect |
| 33. C2×Q8×C59 | C2×C4 | semidirect |
| 51. (C2×D59)⋊C4 | C2×C4 | semidirect |
| 57. C4×Dic59 | C2×C4 | semidirect |
| 105. Dic59 | #124 | semidirect |
| 116. #391 | D59 | semidirect |
| 122. C59 | C4×#124 | semidirect |
| 146. C2×Q8 | C4×D59 | semidirect |