Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447440 | C2 | semidirect |
| 3. #21443803 | C2 | semidirect |
| 4. C61×#1812 | C2 | semidirect |
| 5. C22×D488 | C4 | semidirect |
| 8. #16840015 | C4 | semidirect |
| 12. #16839800 | C4 | semidirect |
| 15. #16839544 | C22 | semidirect |
| 19. C61×H(3,ℤ/4) | C22 | semidirect |
| 147. #1812 | D61 | semidirect |
| 169. H(3,ℤ/4) | C2×D61 | semidirect |
| 170. C61 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455467 | 2 |
| #21447440 | 2 |
| #21443803 | 2 |
| C61×#1812 | 2 |
| #11868 | 61 |