Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
702 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 235 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 |
|---|---|---|
| 3. #21446383 | C2 | semidirect |
| 4. #21445964 | C2 | semidirect |
| 5. C8×#11758196 | C2 | semidirect |
| 7. C61×#1726 | C2 | semidirect |
| 119. #1726 | D61 | semidirect |
| 141. C61 | #21668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21449117 | 2 |
| #21446432 | 2 |
| #21446383 | 2 |
| #21445964 | 2 |
| C8×#11758196 | 2 |
| C8×#11758198 | 2 |
| C61×#1726 | 2 |
| #21668 | 61 |