Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21446640 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443649 | C2 | semidirect |
| 7. C61×#1546 | C2 | semidirect |
| 10. #16840165 | C4 | semidirect |
| 11. #16840110 | C4 | semidirect |
| 179. #1546 | D61 | semidirect |
| 208. C61 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456940 | 2 |
| #21454536 | 2 |
| #21446640 | 2 |
| #21444380 | 2 |
| #21443679 | 2 |
| #21443649 | 2 |
| C61×#1546 | 2 |
| #9291 | 61 |