Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21448044 | C2 | semidirect |
| 3. #21447963 | C2 | semidirect |
| 4. #21443864 | C2 | semidirect |
| 5. #21443779 | C2 | semidirect |
| 6. D4⋊#11758185 | C2 | semidirect |
| 7. C61×#1675 | C2 | semidirect |
| 16. C4⋊#11758185 | C22 | semidirect |
| 19. C4×#11758185 | C22 | semidirect |
| 20. C61×#500 | C22 | semidirect |
| 23. C61×#335 | C22 | semidirect |
| 147. #1675 | D61 | semidirect |
| 159. #500 | C2×D61 | semidirect |
| 172. #335 | C2×D61 | semidirect |
| 174. C61 | #12372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D488 | 2 |
| #21448044 | 2 |
| #21447963 | 2 |
| #21443864 | 2 |
| #21443779 | 2 |
| D4⋊#11758185 | 2 |
| C61×#1675 | 2 |
| #12372 | 61 |