Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 3. #21460853 | C2 | semidirect |
| 4. #21460852 | C2 | semidirect |
| 5. #21460851 | C2 | semidirect |
| 6. #21460850 | C2 | semidirect |
| 64. C16×C61 | M16 | semidirect |
| 66. #11758185 | M16 | semidirect |
| 127. C61 | #12025 | semidirect |
| 171. C16 | #11758217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461381 | 2 |
| #21461376 | 2 |
| #21460853 | 2 |
| #21460852 | 2 |
| #21460851 | 2 |
| #21460850 | 2 |
| M32×Dic61 | 2 |
| #12025 | 61 |