Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
304 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 65 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. C22⋊C8×D163 | C2 | semidirect |
| 3. #23781512 | C2 | semidirect |
| 4. #23781402 | C2 | semidirect |
| 5. #23781400 | C2 | semidirect |
| 6. #23781398 | C2 | semidirect |
| 7. #328×C163 | C2 | semidirect |
| 8. C2×#14579700 | C4 | semidirect |
| 12. #19104711 | C4 | semidirect |
| 13. #19104710 | C4 | semidirect |
| 18. #19104693 | C4 | semidirect |
| 128. C163 | #1501 | semidirect |
| 134. #328 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782178 | 2 |
| C22⋊C8×D163 | 2 |
| #23781512 | 2 |
| #23781402 | 2 |
| #23781400 | 2 |
| #23781398 | 2 |
| #328×C163 | 2 |
| #1501 | 163 |