Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
340 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 340 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. #21458832 | C2 | semidirect |
| 3. #21447860 | C2 | semidirect |
| 4. #21445179 | C2 | semidirect |
| 5. #21443866 | C2 | semidirect |
| 6. #21443784 | C2 | semidirect |
| 7. C61×Q8⋊C16 | C2 | semidirect |
| 140. Q8⋊C16 | D61 | semidirect |
| 164. C61 | #12329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458832 | 2 |
| #21448069 | 2 |
| #21447860 | 2 |
| #21445179 | 2 |
| #21443866 | 2 |
| #21443784 | 2 |
| C61×Q8⋊C16 | 2 |
| #12329 | 61 |