Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
294 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 81 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×C32×D61 | C2 | semidirect |
| 3. #368×D61 | C2 | semidirect |
| 4. #21444004 | C2 | semidirect |
| 5. #21444003 | C2 | semidirect |
| 6. #21444002 | C2 | semidirect |
| 7. C61×#1417 | C2 | semidirect |
| 19. C2×#14519683 | C22 | semidirect |
| 22. #16839592 | C22 | semidirect |
| 25. C2×C32×C61 | C22 | semidirect |
| 26. C61×#368 | C22 | semidirect |
| 144. #1417 | D61 | direct (N × H) |
| 150. D61 | #1417 | direct (N × H) |
| 166. C2×C32 | C2×D61 | semidirect |
| 169. #368 | C2×D61 | semidirect |
| 170. C61 | C2×#1417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D61 | 2 |
| C2×C32×D61 | 2 |
| #368×D61 | 2 |
| #21444004 | 2 |
| #21444003 | 2 |
| #21444002 | 2 |
| C61×#1417 | 2 |
| C2×#1417 | 61 |