Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 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×#19104761 | C2 | semidirect |
| 2. C2×#19104757 | C2 | semidirect |
| 3. #23782232 | C2 | semidirect |
| 4. #23782053 | C2 | semidirect |
| 5. #23782048 | C2 | semidirect |
| 6. #23782040 | C2 | semidirect |
| 7. #23781620 | C2 | semidirect |
| 8. C22×D8×C163 | C2 | semidirect |
| 12. C2×Dic652 | C22 | semidirect |
| 13. C2×#14579688 | C22 | semidirect |
| 14. C2×#14579687 | C22 | semidirect |
| 15. C2×D1304 | C22 | semidirect |
| 16. C2×#14579684 | C22 | semidirect |
| 18. #19104731 | C22 | semidirect |
| 19. #19104722 | C22 | semidirect |
| 23. #19104645 | C22 | semidirect |
| 24. C8×Dic163 | C22 | semidirect |
| 42. #14579683 | D4 | semidirect |
| 56. C2×C8×C163 | D4 | semidirect |
| 101. C163 | #3155 | semidirect |
| 105. C22×D8 | D163 | semidirect |
| 154. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104761 | 2 |
| C2×#19104757 | 2 |
| #23782232 | 2 |
| #23782053 | 2 |
| #23782048 | 2 |
| #23782040 | 2 |
| #23781620 | 2 |
| C22×D8×C163 | 2 |
| #3155 | 163 |