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 |
|---|---|---|
| 2. C2×#16839800 | C2 | semidirect |
| 3. #21448028 | C2 | semidirect |
| 4. #21448011 | C2 | semidirect |
| 5. #21447607 | C2 | semidirect |
| 6. #21447532 | C2 | semidirect |
| 7. C61×#2112 | C2 | semidirect |
| 20. #16839590 | C22 | semidirect |
| 21. #16839588 | C22 | semidirect |
| 22. #16839567 | C22 | semidirect |
| 23. #16839564 | C22 | semidirect |
| 145. #2112 | D61 | semidirect |
| 170. C61 | #33647 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455400 | 2 |
| C2×#16839800 | 2 |
| #21448028 | 2 |
| #21448011 | 2 |
| #21447607 | 2 |
| #21447532 | 2 |
| C61×#2112 | 2 |
| #33647 | 61 |