Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 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. C2×#16839587 | C2 | semidirect |
| 3. C2×#16839569 | C2 | semidirect |
| 4. C2×#16839547 | C2 | semidirect |
| 5. #21445884 | C2 | semidirect |
| 6. #21443928 | C2 | semidirect |
| 7. C61×#2139 | C2 | semidirect |
| 44. C2×#11758185 | D4 | semidirect |
| 180. #2139 | D61 | semidirect |
| 210. C61 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455485 | 2 |
| C2×#16839587 | 2 |
| C2×#16839569 | 2 |
| C2×#16839547 | 2 |
| #21445884 | 2 |
| #21443928 | 2 |
| C61×#2139 | 2 |
| #13384 | 61 |