Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #21443740 | C2 | semidirect |
| 5. #21443739 | C2 | semidirect |
| 6. #21443739 | C2 | semidirect |
| 7. C61×#1313 | C2 | semidirect |
| 62. C16×C61 | M16 | semidirect |
| 102. #1313 | D61 | semidirect |
| 122. C61 | #11414 | semidirect |
| 164. C16 | #11758189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447620 | 2 |
| #21447412 | 2 |
| #21444105 | 2 |
| #21443740 | 2 |
| #21443739 | 2 |
| C61×#1313 | 2 |
| #11414 | 61 |