Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
426 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 215 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. D4×Dic317 | C2 | direct (N × H) |
| 3. C2×C4⋊Dic317 | C2 | semidirect |
| 4. C2×C22⋊Dic317 | C2 | semidirect |
| 5. C2×C4×Dic317 | C2 | semidirect |
| 11. C22×Dic317 | C22 | semidirect |
| 12. C4⋊Dic317 | C22 | semidirect |
| 13. C22⋊Dic317 | C22 | semidirect |
| 14. C4×Dic317 | C22 | semidirect |
| 16. C2×D4×C317 | C4 | semidirect |
| 22. C2×Dic317 | D4 | direct (N × H) |
| 28. C23×C317 | C2×C4 | semidirect |
| 31. D4×C317 | C2×C4 | semidirect |
| 32. C2×C4×C317 | C2×C4 | semidirect |
| 38. C22×C317 | C22×C4 | semidirect |
| 42. C4×C317 | C22×C4 | semidirect |
| 45. Dic317 | C2×D4 | direct (N × H) |
| 47. C2×C317 | C4×D4 | semidirect |
| 51. C317 | C2×C4×D4 | semidirect |
| 60. C2×D4 | Dic317 | direct (N × H) |
| 73. C23 | C2×Dic317 | semidirect |
| 76. D4 | C2×Dic317 | direct (N × H) |
| 84. C2×C4 | C2×Dic317 | semidirect |
| 90. C22 | C22×Dic317 | semidirect |
| 97. C4 | C22×Dic317 | semidirect |
| 99. C2 | D4×Dic317 | 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 |
| D4×Dic317 | 2 |
| C2×C4⋊Dic317 | 2 |
| C2×C22⋊Dic317 | 2 |
| C2×C4×Dic317 | 2 |
| C22×D4×C317 | 2 |
| C2×C4×D4 | 317 |