Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21448293 | C2 | semidirect |
| 4. #21444249 | C2 | semidirect |
| 5. #21443722 | C2 | semidirect |
| 6. #21443651 | C2 | semidirect |
| 10. #16840044 | C4 | semidirect |
| 11. #16839959 | C4 | semidirect |
| 118. C4×Dic61 | SD16 | semidirect |
| 224. C61 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455846 | 2 |
| #21448293 | 2 |
| #21446648 | 2 |
| #21444249 | 2 |
| #21443722 | 2 |
| #21443651 | 2 |
| C61×#1502 | 2 |
| #9238 | 61 |