Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#16839600 | C2 | semidirect |
| 2. C2×#16839597 | C2 | semidirect |
| 3. #21448080 | C2 | semidirect |
| 4. #21443953 | C2 | semidirect |
| 5. C61×#2246 | C2 | semidirect |
| 24. #14519683 | D4 | semidirect |
| 80. #2246 | D61 | semidirect |
| 97. C61 | #13729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839600 | 2 |
| C2×#16839597 | 2 |
| #21448080 | 2 |
| #21443953 | 2 |
| C61×#2246 | 2 |
| #13729 | 61 |