Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
534 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21446633 | C2 | semidirect |
| 3. #21445985 | C2 | semidirect |
| 4. C2×#16839502 | C2 | semidirect |
| 5. C2×#16839501 | C2 | semidirect |
| 6. #21443701 | C2 | semidirect |
| 7. C61×#1959 | C2 | semidirect |
| 54. #14519688 | D4 | semidirect |
| 231. #1959 | D61 | semidirect |
| 266. C61 | #10424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21453864 | 2 |
| #21446633 | 2 |
| #21445985 | 2 |
| C2×#16839502 | 2 |
| C2×#16839501 | 2 |
| #21443701 | 2 |
| C61×#1959 | 2 |
| #10424 | 61 |