Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
572 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21455937 | C2 | semidirect |
| 2. #21451308 | C2 | semidirect |
| 3. #21446739 | C2 | semidirect |
| 4. #21444417 | C2 | semidirect |
| 5. #21444265 | C2 | semidirect |
| 6. #21443676 | C2 | semidirect |
| 249. C61 | #10006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455937 | 2 |
| #21451308 | 2 |
| #21446739 | 2 |
| #21444417 | 2 |
| #21444265 | 2 |
| #21443676 | 2 |
| C61×#3213 | 2 |
| #10006 | 61 |