Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
288 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×Dic976 | C2 | semidirect |
| 3. C2×#16839601 | C2 | semidirect |
| 4. #21447910 | C2 | semidirect |
| 5. #21444001 | C2 | semidirect |
| 6. #21443998 | C2 | semidirect |
| 7. C61×C22⋊C32 | C2 | semidirect |
| 112. C22⋊C32 | D61 | semidirect |
| 133. C61 | #13666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840194 | 2 |
| C2×Dic976 | 2 |
| C2×#16839601 | 2 |
| #21447910 | 2 |
| #21444001 | 2 |
| #21443998 | 2 |
| C61×C22⋊C32 | 2 |
| #13666 | 61 |