Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 474 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. C2×#16839567 | C2 | semidirect |
| 4. #21446732 | C2 | semidirect |
| 5. #21443929 | C2 | semidirect |
| 6. #21443907 | C2 | semidirect |
| 11. #16840202 | C4 | semidirect |
| 34. C2×Dic244 | C2×C4 | semidirect |
| 46. #14519717 | C2×C4 | semidirect |
| 209. C61 | #13023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840202 | 2 |
| #21454695 | 2 |
| C2×#16839567 | 2 |
| #21446732 | 2 |
| #21443929 | 2 |
| #21443907 | 2 |
| C2×C61×#359 | 2 |
| #13023 | 61 |