Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21456478 | C2 | semidirect |
| 3. #21448039 | C2 | semidirect |
| 4. #21447996 | C2 | semidirect |
| 5. #21447901 | C2 | semidirect |
| 7. #21447712 | C2 | semidirect |
| 8. C61×#2166 | C2 | semidirect |
| 13. #16840164 | C22 | semidirect |
| 14. #16840142 | C22 | semidirect |
| 22. #16839870 | C22 | semidirect |
| 26. #16839585 | C22 | semidirect |
| 27. #16839579 | C22 | semidirect |
| 30. C61×#364 | C22 | semidirect |
| 32. C61×#347 | C22 | semidirect |
| 164. #2166 | D61 | semidirect |
| 188. #364 | C2×D61 | semidirect |
| 192. #347 | C2×D61 | semidirect |
| 193. C61 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456478 | 2 |
| #21454723 | 2 |
| #21448039 | 2 |
| #21447996 | 2 |
| #21447901 | 2 |
| #21447772 | 2 |
| #21447712 | 2 |
| C61×#2166 | 2 |
| #33693 | 61 |