Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21447438 | C2 | semidirect |
| 3. #21445868 | C2 | semidirect |
| 4. #21443811 | C2 | semidirect |
| 5. #21443810 | C2 | semidirect |
| 6. #21443809 | C2 | semidirect |
| 7. C61×#1341 | C2 | semidirect |
| 21. #16839544 | C22 | semidirect |
| 23. #16839520 | C22 | semidirect |
| 25. C61×#349 | C22 | semidirect |
| 26. C61×#338 | C22 | semidirect |
| 188. #1341 | D61 | semidirect |
| 212. #349 | C2×D61 | semidirect |
| 214. #338 | C2×D61 | semidirect |
| 215. C61 | #11870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455465 | 2 |
| #21447438 | 2 |
| #21445868 | 2 |
| #21443811 | 2 |
| #21443810 | 2 |
| #21443809 | 2 |
| C61×#1341 | 2 |
| #11870 | 61 |