Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #21444593 | C2 | semidirect |
| 5. #21443729 | C2 | semidirect |
| 6. #21443682 | C2 | semidirect |
| 7. C61×#1290 | C2 | semidirect |
| 121. #1290 | D61 | semidirect |
| 141. C61 | #10645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21444593 | 2 |
| #21444542 | 2 |
| #21444512 | 2 |
| #21444287 | 2 |
| #21443729 | 2 |
| #21443682 | 2 |
| C61×#1290 | 2 |
| #10645 | 61 |