Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782210 | C2 | semidirect |
| 2. #23782069 | C2 | semidirect |
| 3. #23782040 | C2 | semidirect |
| 4. #23782010 | C2 | semidirect |
| 5. #23781901 | C2 | semidirect |
| 6. #23781899 | C2 | semidirect |
| 7. D8×Dic163 | C2 | semidirect |
| 8. #23781747 | C2 | semidirect |
| 9. #23781745 | C2 | semidirect |
| 10. C2×C8×Dic163 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 82. C2×Dic163 | D8 | semidirect |
| 89. C163⋊C8 | #41 | semidirect |
| 101. C8×C163 | #41 | semidirect |
| 127. C163 | #3169 | semidirect |
| 135. #466 | D163 | semidirect |
| 229. C8 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782210 | 2 |
| #23782069 | 2 |
| #23782040 | 2 |
| #23782010 | 2 |
| #23781901 | 2 |
| #23781899 | 2 |
| D8×Dic163 | 2 |
| #23781747 | 2 |
| #23781745 | 2 |
| C2×C8×Dic163 | 2 |
| #466×C163 | 2 |
| #3169 | 163 |