Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#16839574 | C2 | semidirect |
| 3. C2×#16839564 | C2 | semidirect |
| 4. #21447432 | C2 | semidirect |
| 5. #21445880 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C2×C61×#368 | C2 | semidirect |
| 165. C2×#368 | D61 | semidirect |
| 195. C61 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840033 | 2 |
| C2×#16839574 | 2 |
| C2×#16839564 | 2 |
| #21447432 | 2 |
| #21445880 | 2 |
| #21443929 | 2 |
| C2×C61×#368 | 2 |
| #13393 | 61 |