Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21444727 | C2 | semidirect |
| 4. #21443884 | C2 | semidirect |
| 5. #21443790 | C2 | semidirect |
| 6. #21443741 | C2 | semidirect |
| 66. #11758185 | M16 | semidirect |
| 125. C61 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447683 | 2 |
| #21444733 | 2 |
| #21444727 | 2 |
| #21443884 | 2 |
| #21443790 | 2 |
| #21443741 | 2 |
| C61×#1333 | 2 |
| #12087 | 61 |