Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
688 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 688 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 | C2×#120×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#120 | D59 |
| hypocenter | C59 | #2375 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837305 | C2 | semidirect |
| 2. #16837295 | C2 | semidirect |
| 3. #16837282 | C2 | semidirect |
| 4. #16837258 | C2 | semidirect |
| 6. C23×Dic59 | C22 | semidirect |
| 7. C2×C4⋊Dic59 | C22 | semidirect |
| 10. C2×C22⋊Dic59 | C22 | semidirect |
| 11. C2×C4×Dic59 | C22 | semidirect |
| 12. C59⋊#95 | C22 | semidirect |
| 15. #120×C59 | C4 | semidirect |
| 19. C24×C59 | C2×C4 | semidirect |
| 29. C22⋊C4×C59 | C2×C4 | semidirect |
| 82. C59 | #2375 | semidirect |
| 86. #120 | Dic59 | semidirect |
| 96. C24 | C2×Dic59 | semidirect |
| 110. C22⋊C4 | C2×Dic59 | semidirect |