Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21446760 | C2 | semidirect |
| 4. #21444222 | C2 | semidirect |
| 6. #21443649 | C2 | semidirect |
| 7. C61×#3104 | C2 | semidirect |
| 189. #3104 | D61 | semidirect |
| 225. C61 | #10035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456167 | 2 |
| #21455850 | 2 |
| #21446760 | 2 |
| #21444222 | 2 |
| #21444219 | 2 |
| #21443649 | 2 |
| C61×#3104 | 2 |
| #10035 | 61 |