Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104756 | C2 | semidirect |
| 2. #23782335 | C2 | semidirect |
| 3. #23782318 | C2 | semidirect |
| 4. #23781891 | C2 | semidirect |
| 5. #23781872 | C2 | semidirect |
| 6. #23781857 | C2 | semidirect |
| 7. #23781824 | C2 | semidirect |
| 8. #23781809 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. C8×D652 | C2 | semidirect |
| 11. #492×C163 | C2 | semidirect |
| 57. #14579688 | D4 | semidirect |
| 127. C4×C163 | #135 | semidirect |
| 140. C163 | #3284 | semidirect |
| 145. #492 | D163 | semidirect |
| 272. C4 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| #23782335 | 2 |
| #23782318 | 2 |
| #23781891 | 2 |
| #23781872 | 2 |
| #23781857 | 2 |
| #23781824 | 2 |
| #23781809 | 2 |
| C4×#14579688 | 2 |
| C8×D652 | 2 |
| #492×C163 | 2 |
| #3284 | 163 |