Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. Q64×D61 | C2 | semidirect |
| 3. Dic1952 | C2 | semidirect |
| 4. #21444036 | C2 | semidirect |
| 5. #21444034 | C2 | semidirect |
| 6. #21444029 | C2 | semidirect |
| 7. C61×SD128 | C2 | semidirect |
| 65. SD128 | D61 | semidirect |
| 81. C61 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448125 | 2 |
| Q64×D61 | 2 |
| Dic1952 | 2 |
| #21444036 | 2 |
| #21444034 | 2 |
| #21444029 | 2 |
| C61×SD128 | 2 |
| #13743 | 61 |