Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
886 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21447569 | C2 | semidirect |
| 3. C2×#16839570 | C2 | semidirect |
| 4. #21445869 | C2 | semidirect |
| 5. C61×#2113 | C2 | semidirect |
| 14. C2×#14519713 | C22 | semidirect |
| 21. C2×M32×C61 | C22 | semidirect |
| 22. C22×C16×C61 | C22 | semidirect |
| 166. #2113 | D61 | semidirect |
| 182. C2×M32 | C2×D61 | semidirect |
| 183. C22×C16 | C2×D61 | semidirect |
| 191. C61 | #12746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460593 | 2 |
| #21447569 | 2 |
| C2×#16839570 | 2 |
| #21445869 | 2 |
| C61×#2113 | 2 |
| #12746 | 61 |