Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 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. #21458250 | C2 | semidirect |
| 2. #21448043 | C2 | semidirect |
| 3. #21447860 | C2 | semidirect |
| 5. #21443873 | C2 | semidirect |
| 6. #21443784 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 136. D4⋊C16 | D61 | semidirect |
| 159. C61 | #12341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458250 | 2 |
| #21448043 | 2 |
| #21447860 | 2 |
| #21445174 | 2 |
| #21443873 | 2 |
| #21443784 | 2 |
| C61×D4⋊C16 | 2 |
| #12341 | 61 |