Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#19104782 | C2 | semidirect |
| 2. C22×#14579687 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23781807 | C2 | semidirect |
| 5. #23781802 | C2 | semidirect |
| 6. #23781675 | C2 | semidirect |
| 7. #23781661 | C2 | semidirect |
| 8. #23781633 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 15. C2×#14579698 | C22 | semidirect |
| 18. C2×Q8×D163 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 28. #19104659 | C22 | semidirect |
| 29. #19104656 | C22 | semidirect |
| 30. (C2×D163)⋊C8 | C22 | semidirect |
| 48. C2×Dic326 | D4 | semidirect |
| 69. #41×C163 | D4 | semidirect |
| 145. C163 | #3010 | semidirect |
| 148. C2×AGL(1,ℤ/8) | D163 | semidirect |
| 191. #41 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| C22×#14579687 | 2 |
| #23782232 | 2 |
| #23781807 | 2 |
| #23781802 | 2 |
| #23781675 | 2 |
| #23781661 | 2 |
| #23781633 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3010 | 163 |