Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21447617 | C2 | semidirect |
| 3. #21444579 | C2 | semidirect |
| 4. #21443863 | C2 | semidirect |
| 5. #21443862 | C2 | semidirect |
| 6. #21443861 | C2 | semidirect |
| 7. C61×#1360 | C2 | semidirect |
| 19. C4⋊#11758185 | C22 | semidirect |
| 23. #16839513 | C22 | semidirect |
| 25. C61×C4⋊C16 | C22 | semidirect |
| 26. C61×#334 | C22 | semidirect |
| 177. #1360 | D61 | semidirect |
| 197. C4⋊C16 | C2×D61 | semidirect |
| 202. #334 | C2×D61 | semidirect |
| 203. C61 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #495×D61 | 2 |
| #21447617 | 2 |
| #21444579 | 2 |
| #21443863 | 2 |
| #21443862 | 2 |
| #21443861 | 2 |
| C61×#1360 | 2 |
| #11957 | 61 |