Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
502 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21447573 | C2 | semidirect |
| 3. #21444566 | C2 | semidirect |
| 4. #21443866 | C2 | semidirect |
| 5. #21443865 | C2 | semidirect |
| 6. #21443864 | C2 | semidirect |
| 7. C61×#1361 | C2 | semidirect |
| 18. C4⋊#11758185 | C22 | semidirect |
| 20. #16839515 | C22 | semidirect |
| 23. C61×C4⋊C16 | C22 | semidirect |
| 24. C61×#335 | C22 | semidirect |
| 160. #1361 | D61 | semidirect |
| 180. C4⋊C16 | C2×D61 | semidirect |
| 182. #335 | C2×D61 | semidirect |
| 184. C61 | #11931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #493×D61 | 2 |
| #21447573 | 2 |
| #21444566 | 2 |
| #21443866 | 2 |
| #21443865 | 2 |
| #21443864 | 2 |
| C61×#1361 | 2 |
| #11931 | 61 |