Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
310 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 157 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×Dic634 | C2 | semidirect |
| 3. #23778745 | C2 | semidirect |
| 4. D4×Dic317 | C2 | semidirect |
| 5. C4×C22⋊D317 | C2 | semidirect |
| 6. #23778740 | C2 | semidirect |
| 7. #23778738 | C2 | semidirect |
| 8. #23778736 | C2 | semidirect |
| 9. C2×C4×Dic317 | C2 | semidirect |
| 10. C42×D317 | C2 | semidirect |
| 11. C4×D4×C317 | C2 | semidirect |
| 12. #19099573 | C4 | direct (N × H) |
| 37. Dic634 | C2×C4 | semidirect |
| 38. C22⋊D317 | C2×C4 | semidirect |
| 40. C2×Dic317 | C2×C4 | semidirect |
| 48. C4×D317 | C2×C4 | semidirect |
| 50. D4×C317 | C2×C4 | semidirect |
| 66. C4×C317 | #41 | semidirect |
| 71. Dic317 | #41 | semidirect |
| 77. C317 | C4×#41 | semidirect |
| 85. C4×D4 | D317 | semidirect |
| 118. D4 | C4×D317 | semidirect |
| 149. C4 | #19099573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099573 | 2 |
| C4×Dic634 | 2 |
| #23778745 | 2 |
| D4×Dic317 | 2 |
| C4×C22⋊D317 | 2 |
| #23778740 | 2 |
| #23778738 | 2 |
| #23778736 | 2 |
| C2×C4×Dic317 | 2 |
| C42×D317 | 2 |
| C4×D4×C317 | 2 |
| C4×#41 | 317 |