Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
414 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21446749 | C2 | semidirect |
| 3. #21444512 | C2 | semidirect |
| 4. #21444315 | C2 | semidirect |
| 5. #21444170 | C2 | semidirect |
| 6. #21443676 | C2 | semidirect |
| 7. C61×#1573 | C2 | semidirect |
| 189. #1573 | D61 | semidirect |
| 222. C61 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456808 | 2 |
| #21446749 | 2 |
| #21444512 | 2 |
| #21444315 | 2 |
| #21444170 | 2 |
| #21443676 | 2 |
| C61×#1573 | 2 |
| #10508 | 61 |