Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #23782142 | C2 | semidirect |
| 4. #23781767 | C2 | semidirect |
| 5. C4×#14579688 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 9. #405×C163 | C2 | semidirect |
| 12. C2×#14579688 | C4 | semidirect |
| 15. C4×Dic326 | C22 | semidirect |
| 23. #19104669 | C22 | semidirect |
| 24. #19104667 | C22 | semidirect |
| 25. #19104660 | C22 | semidirect |
| 30. #97×C163 | C22 | semidirect |
| 31. C4×C8×C163 | C22 | semidirect |
| 35. C2×Dic326 | C2×C4 | semidirect |
| 43. #14579688 | C2×C4 | semidirect |
| 44. #14579688 | C2×C4 | semidirect |
| 56. C2×C8×C163 | C2×C4 | semidirect |
| 103. C163 | #2949 | semidirect |
| 113. #405 | D163 | semidirect |
| 134. #97 | C2×D163 | semidirect |
| 135. C4×C8 | C2×D163 | semidirect |
| 151. C2×C8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| #23782142 | 2 |
| #23782139 | 2 |
| #23781767 | 2 |
| C4×#14579688 | 2 |
| #23781703 | 2 |
| #23781675 | 2 |
| #23781671 | 2 |
| #405×C163 | 2 |
| #2949 | 163 |