Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
398 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447579 | C2 | semidirect |
| 3. C2×#16839579 | C2 | semidirect |
| 4. #21446732 | C2 | semidirect |
| 6. #21443912 | C2 | semidirect |
| 178. C61 | #13440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519721 | 2 |
| #21447579 | 2 |
| C2×#16839579 | 2 |
| #21446732 | 2 |
| #21446730 | 2 |
| #21443912 | 2 |
| C2×C61×#361 | 2 |
| #13440 | 61 |