Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #21443832 | C2 | semidirect |
| 5. #21443831 | C2 | semidirect |
| 6. #21443830 | C2 | semidirect |
| 7. C61×#1348 | C2 | semidirect |
| 8. C2×Q16×D61 | C4 | semidirect |
| 12. #16840004 | C4 | semidirect |
| 16. #16840000 | C4 | semidirect |
| 18. #107×D61 | C4 | semidirect |
| 185. #1348 | D61 | semidirect |
| 212. C61 | #11887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×D61 | 2 |
| C22⋊C16×D61 | 2 |
| #21445847 | 2 |
| #21443832 | 2 |
| #21443831 | 2 |
| #21443830 | 2 |
| C61×#1348 | 2 |
| #11887 | 61 |