Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 458 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×#16839586 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. C2×#16839544 | C2 | semidirect |
| 6. #21443919 | C2 | semidirect |
| 7. C61×#1811 | C2 | semidirect |
| 40. #14519717 | D4 | semidirect |
| 171. #1811 | D61 | semidirect |
| 196. C61 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840015 | 2 |
| C2×#16839586 | 2 |
| C2×#16839574 | 2 |
| C2×#16839544 | 2 |
| #21443919 | 2 |
| C61×#1811 | 2 |
| #13398 | 61 |