Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#16839574 | C2 | semidirect |
| 3. #21447531 | C2 | semidirect |
| 4. C2×#16839564 | C2 | semidirect |
| 5. #21446605 | C2 | semidirect |
| 6. #21443907 | C2 | semidirect |
| 7. C2×C61×#359 | C2 | semidirect |
| 69. #108×C61 | D4 | semidirect |
| 185. C2×#359 | D61 | semidirect |
| 216. C61 | #13411 | semidirect |
| 253. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456306 | 2 |
| C2×#16839574 | 2 |
| #21447531 | 2 |
| C2×#16839564 | 2 |
| #21446605 | 2 |
| #21443907 | 2 |
| C2×C61×#359 | 2 |
| #13411 | 61 |