Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
168 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 53 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. #21444020 | C2 | semidirect |
| 4. #21444001 | C2 | semidirect |
| 5. #21443999 | C2 | semidirect |
| 7. C61×#1423 | C2 | semidirect |
| 83. #1423 | D61 | semidirect |
| 102. C61 | #13716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447911 | 2 |
| #21447600 | 2 |
| #21444020 | 2 |
| #21444001 | 2 |
| #21443999 | 2 |
| #21443956 | 2 |
| C61×#1423 | 2 |
| #13716 | 61 |