Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16839809 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. C2×#16839543 | C2 | semidirect |
| 6. #21443917 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 54. #14519713 | D4 | semidirect |
| 64. #108×C61 | D4 | semidirect |
| 179. #1383 | D61 | semidirect |
| 204. C61 | #13010 | semidirect |
| 242. #108 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840016 | 2 |
| C2×#16839809 | 2 |
| C2×#16839576 | 2 |
| C2×#16839574 | 2 |
| C2×#16839543 | 2 |
| #21443917 | 2 |
| C61×#1383 | 2 |
| #13010 | 61 |