Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
278 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #21458972 | C2 | semidirect |
| 2. #21448132 | C2 | semidirect |
| 3. C2×#16839600 | C2 | semidirect |
| 4. #21444011 | C2 | semidirect |
| 5. #21444002 | C2 | semidirect |
| 6. #21443961 | C2 | semidirect |
| 7. C61×#2221 | C2 | semidirect |
| 117. #2221 | D61 | semidirect |
| 143. C61 | #13670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458972 | 2 |
| #21448132 | 2 |
| C2×#16839600 | 2 |
| #21444011 | 2 |
| #21444002 | 2 |
| #21443961 | 2 |
| C61×#2221 | 2 |
| #13670 | 61 |