Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
| 5. #21446599 | C2 | semidirect |
| 6. #21443923 | C2 | semidirect |
| 7. C61×#1378 | C2 | semidirect |
| 19. #16839570 | C4 | semidirect |
| 145. #1378 | D61 | semidirect |
| 167. C61 | #12948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454737 | 2 |
| C2×#16839585 | 2 |
| C2×#16839573 | 2 |
| #21447548 | 2 |
| #21446599 | 2 |
| #21443923 | 2 |
| C61×#1378 | 2 |
| #12948 | 61 |