Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 2. #21448043 | C2 | semidirect |
| 3. #21447966 | C2 | semidirect |
| 4. #21445224 | C2 | semidirect |
| 5. #21443864 | C2 | semidirect |
| 6. #21443799 | C2 | semidirect |
| 7. C61×#1331 | C2 | semidirect |
| 137. #1331 | D61 | semidirect |
| 160. C61 | #12384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458793 | 2 |
| #21448043 | 2 |
| #21447966 | 2 |
| #21445224 | 2 |
| #21443864 | 2 |
| #21443799 | 2 |
| C61×#1331 | 2 |
| #12384 | 61 |