Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. #125×D163 | C2 | semidirect |
| 3. #23782033 | C2 | semidirect |
| 4. #23782031 | C2 | semidirect |
| 5. #23782030 | C2 | semidirect |
| 6. #23782021 | C2 | semidirect |
| 7. #23781665 | C2 | semidirect |
| 8. #23781617 | C2 | semidirect |
| 9. #491×C163 | C2 | semidirect |
| 90. C163 | #3142 | semidirect |
| 95. #491 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| #125×D163 | 2 |
| #23782033 | 2 |
| #23782031 | 2 |
| #23782030 | 2 |
| #23782021 | 2 |
| #23781665 | 2 |
| #23781617 | 2 |
| #491×C163 | 2 |
| #3142 | 163 |