Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
408 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782216 | C2 | semidirect |
| 2. #23782200 | C2 | semidirect |
| 3. #23782054 | C2 | semidirect |
| 4. #23782031 | C2 | semidirect |
| 5. #23782027 | C2 | semidirect |
| 6. #23781919 | C2 | semidirect |
| 7. #23781912 | C2 | semidirect |
| 8. #23781752 | C2 | semidirect |
| 9. #23781747 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #501×C163 | C2 | semidirect |
| 110. C8×C163 | #41 | semidirect |
| 137. C163 | #3171 | semidirect |
| 141. #501 | D163 | semidirect |
| 248. C8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| #23782200 | 2 |
| #23782054 | 2 |
| #23782031 | 2 |
| #23782027 | 2 |
| #23781919 | 2 |
| #23781912 | 2 |
| #23781752 | 2 |
| #23781747 | 2 |
| #23781617 | 2 |
| #501×C163 | 2 |
| #3171 | 163 |