Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
596 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23781565 | C2 | semidirect |
| 3. #23781554 | C2 | semidirect |
| 4. #23781550 | C2 | semidirect |
| 5. #23781543 | C2 | semidirect |
| 6. #23781541 | C2 | semidirect |
| 7. C4×C22⋊Dic163 | C2 | semidirect |
| 8. #23781512 | C2 | semidirect |
| 9. #381×C163 | C2 | semidirect |
| 13. #19104709 | C4 | semidirect |
| 38. C2×C22⋊D163 | C2×C4 | semidirect |
| 45. C4⋊Dic163 | C2×C4 | semidirect |
| 51. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 58. C22×C4×C163 | C2×C4 | semidirect |
| 134. C163 | #2333 | semidirect |
| 142. #381 | D163 | semidirect |
| 183. C22×C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104709 | 2 |
| #23781565 | 2 |
| #23781554 | 2 |
| #23781550 | 2 |
| #23781543 | 2 |
| #23781541 | 2 |
| C4×C22⋊Dic163 | 2 |
| #23781512 | 2 |
| #381×C163 | 2 |
| #2333 | 163 |