Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
584 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16839800 | C2 | semidirect |
| 2. #21448024 | C2 | semidirect |
| 3. #21448007 | C2 | semidirect |
| 4. #21447608 | C2 | semidirect |
| 5. #21447531 | C2 | semidirect |
| 6. #21447430 | C2 | semidirect |
| 14. #16839589 | C22 | semidirect |
| 15. #16839587 | C22 | semidirect |
| 16. #16839566 | C22 | semidirect |
| 17. #16839563 | C22 | semidirect |
| 170. C61 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839800 | 2 |
| #21448024 | 2 |
| #21448007 | 2 |
| #21447608 | 2 |
| #21447531 | 2 |
| #21447430 | 2 |
| C61×#3050 | 2 |
| #33647 | 61 |