Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16839589 | C2 | semidirect |
| 5. #21446605 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 19. #16839568 | C4 | semidirect |
| 44. C2×#11758185 | C2×C4 | semidirect |
| 60. #108×C61 | C2×C4 | semidirect |
| 159. #1387 | D61 | semidirect |
| 185. C61 | #12946 | semidirect |
| 212. #108 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454693 | 2 |
| C2×#16839589 | 2 |
| C2×#16839568 | 2 |
| #21447532 | 2 |
| #21446605 | 2 |
| #21443909 | 2 |
| C61×#1387 | 2 |
| #12946 | 61 |