Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 14. #16839585 | C4 | semidirect |
| 138. C61 | #13114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839585 | 2 |
| #21446560 | 2 |
| #21445727 | 2 |
| #21443927 | 2 |
| #21443919 | 2 |
| #21443902 | 2 |
| C61×#1387 | 2 |
| #13114 | 61 |