Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
590 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21458101 | C2 | semidirect |
| 3. #21445370 | C2 | semidirect |
| 4. #21445363 | C2 | semidirect |
| 5. #21445072 | C2 | semidirect |
| 6. #21445065 | C2 | semidirect |
| 7. #21444717 | C2 | semidirect |
| 9. C61×#1710 | C2 | semidirect |
| 164. #1710 | D61 | semidirect |
| 204. C61 | #20306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458542 | 2 |
| #21458101 | 2 |
| #21445370 | 2 |
| #21445363 | 2 |
| #21445072 | 2 |
| #21445065 | 2 |
| #21444717 | 2 |
| #21444705 | 2 |
| C61×#1710 | 2 |
| #20306 | 61 |