Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 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. #23778738 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic317 | C2 | semidirect |
| 5. C2×C4×Dic317 | C2 | semidirect |
| 6. C2×C4⋊C4×C317 | C2 | semidirect |
| 10. C2×C4×D317 | C4 | semidirect |
| 12. C4⋊Dic317 | C22 | semidirect |
| 14. C4×Dic317 | C22 | semidirect |
| 17. C4⋊C4×C317 | C22 | semidirect |
| 26. C4×D317 | C2×C4 | semidirect |
| 44. C2×C317 | #117 | semidirect |
| 49. C317 | C2×#117 | semidirect |
| 54. C2×C4⋊C4 | D317 | semidirect |
| 65. C4⋊C4 | C2×D317 | semidirect |
| 95. C2 | #23778738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D317 | 2 |
| #23778738 | 2 |
| C2×C4⋊Dic317 | 2 |
| C2×#19099551 | 2 |
| C2×C4×Dic317 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C2×#117 | 317 |