Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
250 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 67 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×#16839601 | C2 | semidirect |
| 2. C2×#16839600 | C2 | semidirect |
| 3. C2×#16839599 | C2 | semidirect |
| 4. #21448070 | C2 | semidirect |
| 6. C32×Dic61 | C2 | semidirect |
| 7. C2×C61×SD64 | C2 | semidirect |
| 37. #14519683 | D4 | semidirect |
| 45. C32×C61 | D4 | semidirect |
| 96. Dic61 | SD64 | semidirect |
| 100. C2×SD64 | D61 | semidirect |
| 123. C61 | #13727 | semidirect |
| 146. C32 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839601 | 2 |
| C2×#16839600 | 2 |
| C2×#16839599 | 2 |
| #21448070 | 2 |
| #21448067 | 2 |
| C32×Dic61 | 2 |
| C2×C61×SD64 | 2 |
| #13727 | 61 |