Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
894 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21447439 | C2 | semidirect |
| 3. #21447434 | C2 | semidirect |
| 4. #21447433 | C2 | semidirect |
| 5. C61×#2115 | C2 | semidirect |
| 14. C2×#14519717 | C22 | semidirect |
| 15. C22×#11758185 | C22 | semidirect |
| 20. C2×M32×C61 | C22 | semidirect |
| 162. #2115 | D61 | semidirect |
| 180. C2×M32 | C2×D61 | semidirect |
| 186. C61 | #12684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460530 | 2 |
| #21447439 | 2 |
| #21447434 | 2 |
| #21447433 | 2 |
| C61×#2115 | 2 |
| #12684 | 61 |