Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21444733 | C2 | semidirect |
| 2. #21444643 | C2 | semidirect |
| 3. #21443885 | C2 | semidirect |
| 4. #21443786 | C2 | semidirect |
| 5. #21443786 | C2 | semidirect |
| 6. #21443741 | C2 | semidirect |
| 51. D8×C61 | M16 | semidirect |
| 131. C61 | #12078 | semidirect |
| 160. D8 | #11758194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21444733 | 2 |
| #21444643 | 2 |
| #21443885 | 2 |
| #21443786 | 2 |
| #21443741 | 2 |
| C61×#2177 | 2 |
| #12078 | 61 |