Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
416 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21447428 | C2 | semidirect |
| 3. #21445847 | C2 | semidirect |
| 4. #21443832 | C2 | semidirect |
| 5. #21443830 | C2 | semidirect |
| 6. #21443828 | C2 | semidirect |
| 7. C61×#1347 | C2 | semidirect |
| 8. C2×#14519796 | C4 | semidirect |
| 12. #16840004 | C4 | semidirect |
| 14. #16839995 | C4 | semidirect |
| 17. #16839799 | C4 | semidirect |
| 189. #1347 | D61 | semidirect |
| 217. C61 | #11890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455398 | 2 |
| #21447428 | 2 |
| #21445847 | 2 |
| #21443832 | 2 |
| #21443830 | 2 |
| #21443828 | 2 |
| C61×#1347 | 2 |
| #11890 | 61 |