Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #21445869 | C2 | semidirect |
| 4. #21443947 | C2 | semidirect |
| 5. C61×#1812 | C2 | semidirect |
| 6. C22×#11758189 | C4 | semidirect |
| 13. #16839790 | C4 | semidirect |
| 16. #16839725 | C4 | semidirect |
| 17. #16839717 | C4 | semidirect |
| 183. #1812 | D61 | semidirect |
| 210. C61 | #12806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454520 | 2 |
| #21447458 | 2 |
| #21445869 | 2 |
| #21443947 | 2 |
| C61×#1812 | 2 |
| #12806 | 61 |