Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
406 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16838074 | C2 | semidirect |
| 2. #16837792 | C2 | semidirect |
| 3. #16837776 | C2 | semidirect |
| 4. #16837614 | C2 | semidirect |
| 5. #16837604 | C2 | semidirect |
| 6. #16837602 | C2 | semidirect |
| 7. #16837597 | C2 | semidirect |
| 8. #16837533 | C2 | semidirect |
| 9. #16837500 | C2 | semidirect |
| 10. C4×#11745669 | C2 | semidirect |
| 11. C59×#556 | C2 | semidirect |
| 106. C59⋊C8 | #41 | semidirect |
| 133. #556 | D59 | semidirect |
| 144. C59 | #3397 | semidirect |