Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21446796 | C2 | semidirect |
| 4. #21444507 | C2 | semidirect |
| 6. #21443694 | C2 | semidirect |
| 7. C61×#1831 | C2 | semidirect |
| 95. C42×C61 | SD16 | semidirect |
| 187. #1831 | D61 | semidirect |
| 218. C61 | #10521 | semidirect |
| 304. C42 | #11758190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457136 | 2 |
| #21446796 | 2 |
| #21446647 | 2 |
| #21444507 | 2 |
| #21444494 | 2 |
| #21443694 | 2 |
| C61×#1831 | 2 |
| #10521 | 61 |