Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
490 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21444554 | C2 | semidirect |
| 3. #21443963 | C2 | semidirect |
| 4. C61×#2126 | C2 | semidirect |
| 5. #16840598 | C4 | semidirect |
| 8. #16839939 | C4 | semidirect |
| 13. #16839746 | C4 | semidirect |
| 15. #16839506 | C22 | semidirect |
| 19. C61×#353 | C22 | semidirect |
| 173. #2126 | D61 | semidirect |
| 194. #353 | C2×D61 | semidirect |
| 197. C61 | #13562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455167 | 2 |
| #21444554 | 2 |
| #21443963 | 2 |
| C61×#2126 | 2 |
| #13562 | 61 |