Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×C22⋊D317 | C2 | semidirect |
| 3. #23778740 | C2 | semidirect |
| 4. #23778736 | C2 | semidirect |
| 5. C2×C22⋊Dic317 | C2 | semidirect |
| 6. C22⋊C4×D317 | C2 | semidirect |
| 7. C2×C22⋊C4×C317 | C2 | semidirect |
| 9. C2×C22⋊D317 | C4 | semidirect |
| 13. C22×Dic317 | C22 | semidirect |
| 14. C2×C4×D317 | C22 | semidirect |
| 15. #19099553 | C22 | semidirect |
| 17. C22⋊Dic317 | C22 | semidirect |
| 18. #19099551 | C22 | semidirect |
| 19. C4×Dic317 | C22 | semidirect |
| 21. C22×C4×C317 | C22 | semidirect |
| 23. C22⋊C4×C317 | C22 | semidirect |
| 25. C22×D317 | C2×C4 | semidirect |
| 27. C22⋊D317 | C2×C4 | semidirect |
| 28. C22⋊D317 | C2×C4 | semidirect |
| 30. C2×Dic317 | C2×C4 | semidirect |
| 35. C23×C317 | C2×C4 | semidirect |
| 61. C317 | #518 | semidirect |
| 69. C2×C22⋊C4 | D317 | semidirect |
| 78. C22×C4 | C2×D317 | semidirect |
| 84. C22⋊C4 | C2×D317 | semidirect |
| 90. C23 | C4×D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D317 | 2 |
| C4×C22⋊D317 | 2 |
| #23778740 | 2 |
| #23778736 | 2 |
| C2×C22⋊Dic317 | 2 |
| C22⋊C4×D317 | 2 |
| C2×C22⋊C4×C317 | 2 |
| #518 | 317 |