Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 104 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. #21461756 | C2 | semidirect |
| 2. #21461248 | C2 | semidirect |
| 3. #21461023 | C2 | semidirect |
| 17. #16840142 | C4 | semidirect |
| 18. #16840134 | C4 | semidirect |
| 20. C61×#493 | C4 | semidirect |
| 143. #493 | #6923 | semidirect |
| 153. C61 | #9756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461248 | 2 |
| #21461023 | 2 |
| #21456246 | 2 |
| #9756 | 61 |