Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 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. #21456475 | C2 | semidirect |
| 3. #21448037 | C2 | semidirect |
| 4. #21447996 | C2 | semidirect |
| 5. #21447995 | C2 | semidirect |
| 6. #21447897 | C2 | semidirect |
| 8. #21447713 | C2 | semidirect |
| 9. #21447711 | C2 | semidirect |
| 10. #21447634 | C2 | semidirect |
| 11. C61×#2214 | C2 | semidirect |
| 16. #16840164 | C22 | semidirect |
| 25. #16839869 | C22 | semidirect |
| 30. #16839586 | C22 | semidirect |
| 31. #16839585 | C22 | semidirect |
| 32. #16839583 | C22 | semidirect |
| 33. #16839578 | C22 | semidirect |
| 37. #16839539 | C22 | semidirect |
| 39. C61×#494 | C22 | semidirect |
| 41. C61×#364 | C22 | semidirect |
| 42. C61×#362 | C22 | semidirect |
| 208. #2214 | D61 | semidirect |
| 224. #494 | C2×D61 | semidirect |
| 242. #364 | C2×D61 | semidirect |
| 244. #362 | C2×D61 | semidirect |
| 249. C61 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456475 | 2 |
| #21454717 | 2 |
| #21448037 | 2 |
| #21447996 | 2 |
| #21447995 | 2 |
| #21447897 | 2 |
| #21447768 | 2 |
| #21447713 | 2 |
| #21447711 | 2 |
| #21447634 | 2 |
| C61×#2214 | 2 |
| #33693 | 61 |