Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
716 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 117 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. #21446137 | C2 | semidirect |
| 2. C2×#16839496 | C2 | semidirect |
| 3. #21444075 | C2 | semidirect |
| 4. #21443662 | C2 | semidirect |
| 31. #14519684 | D4 | semidirect |
| 246. C61 | #10403 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21446137 | 2 |
| C2×#16839496 | 2 |
| #21444075 | 2 |
| #21443662 | 2 |
| C61×#2656 | 2 |
| #10403 | 61 |