Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 63 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. #21447738 | C2 | semidirect |
| 3. #21447735 | C2 | semidirect |
| 4. #21447143 | C2 | semidirect |
| 5. #21443827 | C2 | semidirect |
| 6. #21443758 | C2 | semidirect |
| 7. C61×#1347 | C2 | semidirect |
| 139. C2×Dic61 | SD32 | semidirect |
| 177. #1347 | D61 | semidirect |
| 205. C61 | #12161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457125 | 2 |
| #21447738 | 2 |
| #21447735 | 2 |
| #21447143 | 2 |
| #21443827 | 2 |
| #21443758 | 2 |
| C61×#1347 | 2 |
| #12161 | 61 |