Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
200 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 57 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. #21448137 | C2 | semidirect |
| 3. #21447701 | C2 | semidirect |
| 4. #21444017 | C2 | semidirect |
| 5. #21444012 | C2 | semidirect |
| 6. #21444009 | C2 | semidirect |
| 7. C61×#2249 | C2 | semidirect |
| 95. #2249 | D61 | semidirect |
| 119. C61 | #13691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448137 | 2 |
| #21448132 | 2 |
| #21447701 | 2 |
| #21444017 | 2 |
| #21444012 | 2 |
| #21444009 | 2 |
| C61×#2249 | 2 |
| #13691 | 61 |