Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
320 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782253 | C2 | semidirect |
| 2. #23781818 | C2 | semidirect |
| 3. #23781801 | C2 | semidirect |
| 4. #23781574 | C2 | semidirect |
| 5. #23781403 | C2 | semidirect |
| 6. #23781400 | C2 | semidirect |
| 7. #323×C163 | C2 | semidirect |
| 28. C2×Dic326 | D4 | semidirect |
| 32. C2×D652 | D4 | semidirect |
| 43. C4⋊Dic163 | D4 | semidirect |
| 44. C4⋊Dic163 | D4 | semidirect |
| 135. C163 | #1600 | semidirect |
| 143. #323 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782253 | 2 |
| #23781818 | 2 |
| #23781801 | 2 |
| #23781574 | 2 |
| #23781403 | 2 |
| #23781400 | 2 |
| #323×C163 | 2 |
| #1600 | 163 |