Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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×#16839597 | C2 | semidirect |
| 2. C22×#14519683 | C2 | semidirect |
| 3. #21447905 | C2 | semidirect |
| 4. #21444018 | C2 | semidirect |
| 5. #21443997 | C2 | semidirect |
| 6. #21443996 | C2 | semidirect |
| 7. C61×#2215 | C2 | semidirect |
| 28. #14519683 | D4 | semidirect |
| 84. C22×C61 | D32 | semidirect |
| 97. #2215 | D61 | semidirect |
| 120. C61 | #13694 | semidirect |
| 186. C22 | #16839597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839597 | 2 |
| C22×#14519683 | 2 |
| #21447905 | 2 |
| #21444018 | 2 |
| #21443997 | 2 |
| #21443996 | 2 |
| C61×#2215 | 2 |
| #13694 | 61 |