Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
500 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16839809 | C2 | semidirect |
| 3. #21447547 | C2 | semidirect |
| 4. C2×#16839543 | C2 | semidirect |
| 5. #21443934 | C2 | semidirect |
| 6. #21443933 | C2 | semidirect |
| 7. C61×#2143 | C2 | semidirect |
| 50. #14519713 | D4 | semidirect |
| 70. #108×C61 | D4 | semidirect |
| 182. #2143 | D61 | semidirect |
| 211. C61 | #12998 | semidirect |
| 251. #108 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455424 | 2 |
| C2×#16839809 | 2 |
| #21447547 | 2 |
| C2×#16839543 | 2 |
| #21443934 | 2 |
| #21443933 | 2 |
| C61×#2143 | 2 |
| #12998 | 61 |