Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 61 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×Q32×D61 | C2 | semidirect |
| 2. C2×#16839601 | C2 | semidirect |
| 3. C2×#16839599 | C2 | semidirect |
| 5. #21443999 | C2 | semidirect |
| 6. #21443956 | C2 | semidirect |
| 7. C61×#1416 | C2 | semidirect |
| 32. Dic488 | D4 | semidirect |
| 43. Q32×C61 | D4 | semidirect |
| 100. C2×D61 | SD64 | semidirect |
| 112. #1416 | D61 | semidirect |
| 134. C61 | #13662 | semidirect |
| 148. Q32 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D61 | 2 |
| C2×#16839601 | 2 |
| C2×#16839599 | 2 |
| #21447906 | 2 |
| #21443999 | 2 |
| #21443956 | 2 |
| C61×#1416 | 2 |
| #13662 | 61 |