Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
496 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21447540 | C2 | semidirect |
| 4. #21446732 | C2 | semidirect |
| 5. #21443916 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 12. C2×#14519721 | C4 | semidirect |
| 32. C2×Dic244 | C2×C4 | semidirect |
| 42. C2×#11758185 | C2×C4 | semidirect |
| 186. C61 | #13019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519721 | 2 |
| #21454671 | 2 |
| #21447540 | 2 |
| #21446732 | 2 |
| #21443916 | 2 |
| #21443909 | 2 |
| C2×C61×#361 | 2 |
| #13019 | 61 |