Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
906 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 906 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21456397 | C2 | semidirect |
| 2. #21456396 | C2 | semidirect |
| 3. #21456246 | C2 | semidirect |
| 4. #21456242 | C2 | semidirect |
| 5. #21445492 | C2 | semidirect |
| 6. #21445490 | C2 | semidirect |
| 7. #21445488 | C2 | semidirect |
| 8. #21445486 | C2 | semidirect |
| 9. #21445484 | C2 | semidirect |
| 10. #322×D61 | C2 | semidirect |
| 11. C61×#1721 | C2 | semidirect |
| 135. C8×D61 | D8 | semidirect |
| 196. #1721 | D61 | semidirect |
| 235. C61 | #19616 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456397 | 2 |
| #21456396 | 2 |
| #21456246 | 2 |
| #21456242 | 2 |
| #21445492 | 2 |
| #21445490 | 2 |
| #21445488 | 2 |
| #21445486 | 2 |
| #21445484 | 2 |
| #322×D61 | 2 |
| C61×#1721 | 2 |
| #19616 | 61 |