Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
760 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21446804 | C2 | semidirect |
| 4. #21444340 | C2 | semidirect |
| 5. #21443726 | C2 | semidirect |
| 6. #21443705 | C2 | semidirect |
| 8. C2×#14519807 | C4 | semidirect |
| 14. #16839763 | C4 | semidirect |
| 29. C22×Dic122 | C2×C4 | semidirect |
| 34. C2×#11758194 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic61 | C2×C4 | semidirect |
| 255. C61 | #9361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455079 | 2 |
| #21448649 | 2 |
| #21446804 | 2 |
| #21444340 | 2 |
| #21443726 | 2 |
| #21443705 | 2 |
| C61×#1789 | 2 |
| #9361 | 61 |