Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×D1304 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782234 | C2 | semidirect |
| 4. #23781919 | C2 | semidirect |
| 5. #23781902 | C2 | semidirect |
| 6. #23781669 | C2 | semidirect |
| 7. #427×C163 | C2 | semidirect |
| 15. C2×#14579682 | C22 | semidirect |
| 16. C2×C8×D163 | C22 | semidirect |
| 19. #19104710 | C22 | semidirect |
| 21. #19104655 | C22 | semidirect |
| 24. #107×C163 | C22 | semidirect |
| 25. #106×C163 | C22 | semidirect |
| 46. C2×C8×C163 | D4 | semidirect |
| 93. C163 | #3058 | semidirect |
| 100. #427 | D163 | semidirect |
| 117. #107 | C2×D163 | semidirect |
| 118. #106 | C2×D163 | semidirect |
| 139. C2×C8 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1304 | 2 |
| C2×#19104741 | 2 |
| #23782234 | 2 |
| #23781919 | 2 |
| #23781902 | 2 |
| #23781669 | 2 |
| #427×C163 | 2 |
| #3058 | 163 |