Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
734 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 192 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. #21462541 | C2 | semidirect |
| 2. #21461469 | C2 | semidirect |
| 3. #21461415 | C2 | semidirect |
| 4. #21461374 | C2 | semidirect |
| 5. #21461165 | C2 | semidirect |
| 6. #21461013 | C2 | semidirect |
| 114. C8×C61 | #131 | semidirect |
| 163. C61 | #17962 | semidirect |
| 251. C8 | #14519864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462541 | 2 |
| #21461469 | 2 |
| #21461415 | 2 |
| #21461374 | 2 |
| #21461165 | 2 |
| #21461013 | 2 |
| #21456396 | 2 |
| #17962 | 61 |