Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #21456533 | C2 | semidirect |
| 2. #21456212 | C2 | semidirect |
| 3. #21456200 | C2 | semidirect |
| 4. #21445469 | C2 | semidirect |
| 5. #21445463 | C2 | semidirect |
| 6. #21445457 | C2 | semidirect |
| 7. #21445430 | C2 | semidirect |
| 8. #21444122 | C2 | semidirect |
| 197. C61 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456533 | 2 |
| #21456212 | 2 |
| #21456200 | 2 |
| #21445469 | 2 |
| #21445463 | 2 |
| #21445457 | 2 |
| #21445430 | 2 |
| #21444122 | 2 |
| C61×#3184 | 2 |
| #19754 | 61 |