Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#19104758 | C2 | semidirect |
| 2. #23782326 | C2 | semidirect |
| 3. #23782050 | C2 | semidirect |
| 4. #23781903 | C2 | semidirect |
| 5. #23781901 | C2 | semidirect |
| 6. #23781889 | C2 | semidirect |
| 7. #23781826 | C2 | semidirect |
| 8. #23781804 | C2 | semidirect |
| 9. Q16×Dic163 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. C22×Q16×C163 | C2 | semidirect |
| 76. Q16×C163 | D4 | semidirect |
| 113. C22×C163 | #135 | semidirect |
| 136. C163 | #3285 | semidirect |
| 139. C22×Q16 | D163 | semidirect |
| 195. Q16 | C22⋊D163 | semidirect |
| 256. C22 | #19104758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| #23782326 | 2 |
| #23782050 | 2 |
| #23781903 | 2 |
| #23781901 | 2 |
| #23781889 | 2 |
| #23781826 | 2 |
| #23781804 | 2 |
| Q16×Dic163 | 2 |
| C8×C22⋊D163 | 2 |
| C22×Q16×C163 | 2 |
| #3285 | 163 |