Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
352 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 101 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. #21447616 | C2 | semidirect |
| 3. #21447573 | C2 | semidirect |
| 4. #21443799 | C2 | semidirect |
| 5. #21443797 | C2 | semidirect |
| 6. D4⋊#11758185 | C2 | semidirect |
| 7. C61×D4⋊C16 | C2 | semidirect |
| 105. D4×C61 | M32 | semidirect |
| 126. Dic122 | M32 | semidirect |
| 159. D4⋊C16 | D61 | semidirect |
| 184. C61 | #11623 | semidirect |
| 266. D4 | #14519716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#11758224 | 2 |
| #21447616 | 2 |
| #21447573 | 2 |
| #21443799 | 2 |
| #21443797 | 2 |
| D4⋊#11758185 | 2 |
| C61×D4⋊C16 | 2 |
| #11623 | 61 |