Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
520 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 520 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. #21456562 | C2 | semidirect |
| 3. #21448037 | C2 | semidirect |
| 4. #21447991 | C2 | semidirect |
| 5. #21447990 | C2 | semidirect |
| 6. #21447897 | C2 | semidirect |
| 8. #21447713 | C2 | semidirect |
| 9. #21447711 | C2 | semidirect |
| 10. #21447630 | C2 | semidirect |
| 11. C61×#2214 | C2 | semidirect |
| 16. #16840160 | C22 | semidirect |
| 26. #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 |
| 214. #2214 | D61 | semidirect |
| 230. #494 | C2×D61 | semidirect |
| 248. #364 | C2×D61 | semidirect |
| 250. #362 | C2×D61 | semidirect |
| 255. C61 | #33689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456562 | 2 |
| #21454724 | 2 |
| #21448037 | 2 |
| #21447991 | 2 |
| #21447990 | 2 |
| #21447897 | 2 |
| #21447768 | 2 |
| #21447713 | 2 |
| #21447711 | 2 |
| #21447630 | 2 |
| C61×#2214 | 2 |
| #33689 | 61 |