Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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. C4×C16×D61 | C2 | semidirect |
| 3. #21444576 | C2 | semidirect |
| 4. #21443781 | C2 | semidirect |
| 5. #21443780 | C2 | semidirect |
| 6. #21443779 | C2 | semidirect |
| 7. C61×#1331 | C2 | semidirect |
| 166. #1331 | D61 | semidirect |
| 192. C61 | #11671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456395 | 2 |
| C4×C16×D61 | 2 |
| #21444576 | 2 |
| #21443781 | 2 |
| #21443780 | 2 |
| #21443779 | 2 |
| C61×#1331 | 2 |
| #11671 | 61 |