Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
204 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. C2×#16839601 | C2 | semidirect |
| 2. #21447910 | C2 | semidirect |
| 4. #21444021 | C2 | semidirect |
| 5. #21444001 | C2 | semidirect |
| 6. #21443998 | C2 | semidirect |
| 7. C22×C32×C61 | C2 | semidirect |
| 39. C32×C61 | D4 | semidirect |
| 80. C22×C61 | SD64 | semidirect |
| 92. C22×C32 | D61 | semidirect |
| 116. C61 | #13696 | semidirect |
| 135. C32 | C22⋊D61 | semidirect |
| 178. C22 | #16839601 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839601 | 2 |
| #21447910 | 2 |
| #21447905 | 2 |
| #21444021 | 2 |
| #21444001 | 2 |
| #21443998 | 2 |
| C22×C32×C61 | 2 |
| #13696 | 61 |