Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
252 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 63 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×#16839601 | C2 | semidirect |
| 2. C2×#16839600 | C2 | semidirect |
| 3. C2×#16839597 | C2 | semidirect |
| 4. #21448077 | C2 | semidirect |
| 5. #21448067 | C2 | semidirect |
| 6. #21443952 | C2 | semidirect |
| 7. C2×C61×D32 | C2 | semidirect |
| 37. #14519683 | D4 | semidirect |
| 45. C32×C61 | D4 | semidirect |
| 101. C2×D32 | D61 | semidirect |
| 125. C61 | #13729 | semidirect |
| 148. C32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839601 | 2 |
| C2×#16839600 | 2 |
| C2×#16839597 | 2 |
| #21448077 | 2 |
| #21448067 | 2 |
| #21443952 | 2 |
| C2×C61×D32 | 2 |
| #13729 | 61 |