Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. C2×#16839574 | C2 | semidirect |
| 3. #21447536 | C2 | semidirect |
| 4. #21447446 | C2 | semidirect |
| 5. #21445874 | C2 | semidirect |
| 6. #21443920 | C2 | semidirect |
| 7. C61×#2155 | C2 | semidirect |
| 57. C2×C16×C61 | D4 | semidirect |
| 161. #2155 | D61 | semidirect |
| 190. C61 | #13396 | semidirect |
| 219. C2×C16 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455468 | 2 |
| C2×#16839574 | 2 |
| #21447536 | 2 |
| #21447446 | 2 |
| #21445874 | 2 |
| #21443920 | 2 |
| C61×#2155 | 2 |
| #13396 | 61 |