Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447591 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. #21447534 | C2 | semidirect |
| 5. #21447448 | C2 | semidirect |
| 6. #21445870 | C2 | semidirect |
| 7. C61×#1384 | C2 | semidirect |
| 47. C2×#11758185 | D4 | semidirect |
| 166. #1384 | D61 | semidirect |
| 190. C61 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455468 | 2 |
| #21447591 | 2 |
| C2×#16839576 | 2 |
| #21447534 | 2 |
| #21447448 | 2 |
| #21445870 | 2 |
| C61×#1384 | 2 |
| #13396 | 61 |