Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447511 | C2 | semidirect |
| 3. #21447510 | C2 | semidirect |
| 4. #21447468 | C2 | semidirect |
| 5. #21445867 | C2 | semidirect |
| 6. #21445621 | C2 | semidirect |
| 7. C61×#2122 | C2 | semidirect |
| 8. C22×#11758199 | C4 | semidirect |
| 16. #16839798 | C4 | semidirect |
| 17. #16839767 | C4 | semidirect |
| 18. #16839766 | C4 | semidirect |
| 215. #2122 | D61 | semidirect |
| 248. C61 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455464 | 2 |
| #21447511 | 2 |
| #21447510 | 2 |
| #21447468 | 2 |
| #21445867 | 2 |
| #21445621 | 2 |
| C61×#2122 | 2 |
| #13234 | 61 |