Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16839584 | C2 | semidirect |
| 5. #21443931 | C2 | semidirect |
| 6. #21443922 | C2 | semidirect |
| 7. C2×C61×#365 | C2 | semidirect |
| 18. #16839547 | C4 | semidirect |
| 137. C2×#365 | D61 | semidirect |
| 163. C61 | #12933 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454427 | 2 |
| C2×#16839584 | 2 |
| #21447448 | 2 |
| #21445879 | 2 |
| #21443931 | 2 |
| #21443922 | 2 |
| C2×C61×#365 | 2 |
| #12933 | 61 |