Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
546 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 167 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. #21448038 | C2 | semidirect |
| 3. #21448033 | C2 | semidirect |
| 4. C2×#16839586 | C2 | semidirect |
| 5. #21447566 | C2 | semidirect |
| 6. #21447440 | C2 | semidirect |
| 7. C61×#2916 | C2 | semidirect |
| 141. #2916 | D61 | semidirect |
| 170. C61 | #33659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455481 | 2 |
| #21448038 | 2 |
| #21448033 | 2 |
| C2×#16839586 | 2 |
| #21447566 | 2 |
| #21447440 | 2 |
| C61×#2916 | 2 |
| #33659 | 61 |