Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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×#390 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #390 | D59 |
| hypocenter | C59 | #2328 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×D4×Dic59 | C2 | semidirect |
| 3. C2×#14273689 | C2 | semidirect |
| 4. #16837304 | C2 | semidirect |
| 5. #16837279 | C2 | semidirect |
| 6. #16837278 | C2 | semidirect |
| 7. #16837267 | C2 | semidirect |
| 8. #16837248 | C2 | semidirect |
| 9. C59×#390 | C2 | semidirect |
| 14. #14273723 | C4 | semidirect |
| 34. C2×D4×C59 | C2×C4 | semidirect |
| 40. C2×C22⋊D59 | C2×C4 | semidirect |
| 49. C2×D236 | C2×C4 | semidirect |
| 59. C4×Dic59 | C2×C4 | semidirect |
| 60. C4×Dic59 | D4 | semidirect |
| 128. #390 | D59 | semidirect |
| 133. C59 | #2328 | semidirect |
| 164. C2×D4 | C4×D59 | semidirect |