Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. #21455293 | C2 | semidirect |
| 3. #21450821 | C2 | semidirect |
| 4. #21444488 | C2 | semidirect |
| 5. #21444313 | C2 | semidirect |
| 6. #21444213 | C2 | semidirect |
| 7. C61×#1303 | C2 | semidirect |
| 113. C2×Dic122 | D8 | semidirect |
| 226. #1303 | D61 | semidirect |
| 257. C61 | #10242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456739 | 2 |
| #21455293 | 2 |
| #21450821 | 2 |
| #21444488 | 2 |
| #21444313 | 2 |
| #21444213 | 2 |
| C61×#1303 | 2 |
| #10242 | 61 |