Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 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. C23×Dic317 | C2 | semidirect |
| 2. #23778761 | C2 | direct (N × H) |
| 3. C2×#19099553 | C2 | semidirect |
| 4. C2×C22⋊Dic317 | C2 | semidirect |
| 5. C2×C22⋊Dic317 | C2 | semidirect |
| 10. C22×Dic317 | C22 | semidirect |
| 11. #19099553 | C22 | semidirect |
| 12. C22⋊Dic317 | C22 | semidirect |
| 13. C22⋊Dic317 | C22 | semidirect |
| 48. C2×C317 | #123 | semidirect |
| 51. C317 | C2×#123 | semidirect |
| 100. C2 | #23778761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic317 | 2 |
| #23778761 | 2 |
| C2×#19099553 | 2 |
| C2×C22⋊Dic317 | 2 |
| C22×D4×C317 | 2 |
| C2×#123 | 317 |