Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16839585 | C2 | semidirect |
| 3. C2×#16839584 | C2 | semidirect |
| 6. #21443919 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 19. #16839541 | C4 | semidirect |
| 146. #1383 | D61 | semidirect |
| 168. C61 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839797 | 2 |
| C2×#16839585 | 2 |
| C2×#16839584 | 2 |
| #21447429 | 2 |
| #21445854 | 2 |
| #21443919 | 2 |
| C61×#1383 | 2 |
| #12930 | 61 |