Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
252 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 252 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 |
|---|---|---|
| 13. #16839586 | C4 | semidirect |
| 126. C61 | #13115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447593 | 2 |
| #21446572 | 2 |
| #21443935 | 2 |
| #21443932 | 2 |
| #21443920 | 2 |
| #21443903 | 2 |
| C61×#1773 | 2 |
| #13115 | 61 |