Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
440 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 100 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. #21461752 | C2 | semidirect |
| 3. #21461370 | C2 | semidirect |
| 5. #21460665 | C2 | semidirect |
| 6. #21460647 | C2 | semidirect |
| 92. M16×C61 | M16 | semidirect |
| 110. C4×Dic61 | M16 | semidirect |
| 217. C61 | #8841 | semidirect |
| 276. M16 | #11758217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462738 | 2 |
| #21461752 | 2 |
| #21461370 | 2 |
| #21461114 | 2 |
| #21460665 | 2 |
| #21460647 | 2 |
| #104×Dic61 | 2 |
| #8841 | 61 |