Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
366 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 366 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. #21447962 | C2 | semidirect |
| 4. #21445208 | C2 | semidirect |
| 5. #21443866 | C2 | semidirect |
| 6. #21443784 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 83. Dic244 | SD16 | semidirect |
| 143. D4⋊C16 | D61 | semidirect |
| 166. C61 | #12369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457579 | 2 |
| #21448043 | 2 |
| #21447962 | 2 |
| #21445208 | 2 |
| #21443866 | 2 |
| #21443784 | 2 |
| C61×D4⋊C16 | 2 |
| #12369 | 61 |