Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23782334 | C2 | semidirect |
| 3. #23782040 | C2 | semidirect |
| 4. #23781901 | C2 | semidirect |
| 5. #23781898 | C2 | semidirect |
| 6. #23781863 | C2 | semidirect |
| 7. #23781810 | C2 | semidirect |
| 8. #23781809 | C2 | semidirect |
| 9. Q16×Dic163 | C2 | semidirect |
| 10. C8×C22⋊D163 | C2 | semidirect |
| 11. C2×#135×C163 | C2 | semidirect |
| 74. Q16×C163 | D4 | semidirect |
| 134. Dic163 | #135 | semidirect |
| 142. C163 | #3287 | semidirect |
| 145. C2×#135 | D163 | semidirect |
| 202. Q16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| #23782334 | 2 |
| #23782040 | 2 |
| #23781901 | 2 |
| #23781898 | 2 |
| #23781863 | 2 |
| #23781810 | 2 |
| #23781809 | 2 |
| Q16×Dic163 | 2 |
| C8×C22⋊D163 | 2 |
| C2×#135×C163 | 2 |
| #3287 | 163 |