Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
432 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21447605 | C2 | semidirect |
| 3. C2×#16839571 | C2 | semidirect |
| 4. #21447529 | C2 | semidirect |
| 5. C2×#16839544 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 7. C61×#1809 | C2 | semidirect |
| 49. #14519717 | D4 | semidirect |
| 206. #1809 | D61 | semidirect |
| 236. C61 | #13386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455428 | 2 |
| #21447605 | 2 |
| C2×#16839571 | 2 |
| #21447529 | 2 |
| C2×#16839544 | 2 |
| #21443926 | 2 |
| C61×#1809 | 2 |
| #13386 | 61 |