Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21456734 | C2 | semidirect |
| 2. #21456272 | C2 | semidirect |
| 3. #21446745 | C2 | semidirect |
| 4. #21446739 | C2 | semidirect |
| 5. #21444314 | C2 | semidirect |
| 6. #21443669 | C2 | semidirect |
| 7. C61×#3245 | C2 | semidirect |
| 133. #11758194 | D8 | semidirect |
| 213. #3245 | D61 | semidirect |
| 251. C61 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21456272 | 2 |
| #21446745 | 2 |
| #21446739 | 2 |
| #21444314 | 2 |
| #21443669 | 2 |
| C61×#3245 | 2 |
| #10192 | 61 |