Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #21448999 | C2 | semidirect |
| 3. #21444537 | C2 | semidirect |
| 5. #21443685 | C2 | semidirect |
| 6. #21443683 | C2 | semidirect |
| 10. #16840112 | C4 | semidirect |
| 11. #16840108 | C4 | semidirect |
| 175. C61 | #9430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456212 | 2 |
| #21448999 | 2 |
| #21444537 | 2 |
| #21444366 | 2 |
| #21443685 | 2 |
| #21443683 | 2 |
| C61×#1514 | 2 |
| #9430 | 61 |