Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
764 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 213 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. C2×M16×D163 | C2 | semidirect |
| 3. #23781630 | C2 | semidirect |
| 4. #23781629 | C2 | semidirect |
| 5. #23781628 | C2 | semidirect |
| 6. #407×C163 | C2 | semidirect |
| 17. C2×#14579682 | C22 | semidirect |
| 19. C2×C8×D163 | C22 | semidirect |
| 20. C22⋊(C163⋊C8) | C22 | semidirect |
| 21. (C2×D163)⋊C8 | C22 | semidirect |
| 24. C22⋊C8×C163 | C22 | semidirect |
| 113. C163 | #2879 | semidirect |
| 120. #407 | D163 | semidirect |
| 138. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×M16×D163 | 2 |
| #23781630 | 2 |
| #23781629 | 2 |
| #23781628 | 2 |
| #407×C163 | 2 |
| #2879 | 163 |