Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
298 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21448047 | C2 | semidirect |
| 3. #21447870 | C2 | semidirect |
| 5. #21443876 | C2 | semidirect |
| 6. #21443784 | C2 | semidirect |
| 87. D4×C61 | Q32 | semidirect |
| 152. C61 | #12346 | semidirect |
| 220. D4 | Dic488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458212 | 2 |
| #21448047 | 2 |
| #21447870 | 2 |
| #21445184 | 2 |
| #21443876 | 2 |
| #21443784 | 2 |
| C61×D4⋊C16 | 2 |
| #12346 | 61 |