Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 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 | #2374 |
| 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. #16837296 | C2 | semidirect |
| 3. #16837296 | C2 | semidirect |
| 4. #16837283 | C2 | semidirect |
| 6. C4×Dic59⋊C4 | C2 | semidirect |
| 7. C22⋊C4×Dic59 | C2 | semidirect |
| 8. C22⋊C4×Dic59 | C2 | semidirect |
| 12. #14273708 | C4 | semidirect |
| 44. C22×Dic59 | C2×C4 | semidirect |
| 56. C22⋊Dic59 | C2×C4 | semidirect |
| 58. Dic59⋊C4 | C2×C4 | semidirect |
| 136. C59 | #2374 | semidirect |