Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. C2×#16839565 | C2 | semidirect |
| 5. #21446732 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C61×#1387 | C2 | semidirect |
| 12. #16840205 | C4 | semidirect |
| 39. C2×Dic244 | C2×C4 | semidirect |
| 66. M32×C61 | C2×C4 | semidirect |
| 181. #1387 | D61 | semidirect |
| 209. C61 | #13023 | semidirect |
| 238. M32 | C4×D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840205 | 2 |
| #21454693 | 2 |
| C2×#16839568 | 2 |
| C2×#16839565 | 2 |
| #21446732 | 2 |
| #21443909 | 2 |
| C61×#1387 | 2 |
| #13023 | 61 |