Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
360 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 69 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. #21448043 | C2 | semidirect |
| 3. #21447972 | C2 | semidirect |
| 4. #21445218 | C2 | semidirect |
| 5. #21443866 | C2 | semidirect |
| 6. #21443784 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 141. D4⋊C16 | D61 | semidirect |
| 164. C61 | #12373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457579 | 2 |
| #21448043 | 2 |
| #21447972 | 2 |
| #21445218 | 2 |
| #21443866 | 2 |
| #21443784 | 2 |
| C61×D4⋊C16 | 2 |
| #12373 | 61 |