Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447568 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. #21446610 | C2 | semidirect |
| 6. #21443906 | C2 | semidirect |
| 7. C61×#2143 | C2 | semidirect |
| 67. #108×C61 | D4 | semidirect |
| 173. #2143 | D61 | semidirect |
| 201. C61 | #13417 | semidirect |
| 240. #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 |
| #21447568 | 2 |
| C2×#16839576 | 2 |
| C2×#16839574 | 2 |
| #21446610 | 2 |
| #21443906 | 2 |
| C61×#2143 | 2 |
| #13417 | 61 |