Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
286 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #21448106 | C2 | semidirect |
| 2. #21447956 | C2 | semidirect |
| 3. #21445342 | C2 | semidirect |
| 4. #21443871 | C2 | semidirect |
| 5. #21443786 | C2 | semidirect |
| 6. #21443777 | C2 | semidirect |
| 167. C61 | #12400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448106 | 2 |
| #21447956 | 2 |
| #21445342 | 2 |
| #21443871 | 2 |
| #21443786 | 2 |
| #21443777 | 2 |
| C61×#3355 | 2 |
| #12400 | 61 |