Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
886 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 886 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 1. #21447568 | C2 | semidirect |
| 2. C2×#16839569 | C2 | semidirect |
| 3. #21447433 | C2 | semidirect |
| 4. #21445869 | C2 | semidirect |
| 6. C2×#14519717 | C22 | semidirect |
| 7. C22×#11758185 | C22 | semidirect |
| 8. C2×#14519713 | C22 | semidirect |
| 191. C61 | #12746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447568 | 2 |
| C2×#16839569 | 2 |
| #21447433 | 2 |
| #21445869 | 2 |
| C61×#3584 | 2 |
| #12746 | 61 |