Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16837936 | C2 | semidirect |
| 2. #16837702 | C2 | semidirect |
| 3. #16837694 | C2 | semidirect |
| 4. #16837689 | C2 | semidirect |
| 5. #16837636 | C2 | semidirect |
| 6. #16837629 | C2 | semidirect |
| 7. #16837617 | C2 | semidirect |
| 8. #16837599 | C2 | semidirect |
| 9. #16837594 | C2 | semidirect |
| 10. C2×C4⋊(C59⋊C8) | C2 | semidirect |
| 11. C59×#532 | C2 | semidirect |
| 142. #532 | D59 | semidirect |
| 153. C59 | #3247 | semidirect |