Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
444 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23782139 | C2 | semidirect |
| 3. #23781670 | C2 | semidirect |
| 4. C2×#19104651 | C2 | semidirect |
| 5. #23781426 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #418×C163 | C2 | semidirect |
| 12. #19104731 | C4 | semidirect |
| 38. C4⋊Dic163 | D4 | semidirect |
| 43. C4×Dic163 | C2×C4 | semidirect |
| 50. C2×D4×C163 | C2×C4 | semidirect |
| 55. C4⋊C4×C163 | D4 | semidirect |
| 114. C163 | #1887 | semidirect |
| 119. #418 | D163 | semidirect |
| 154. C2×D4 | C4×D163 | semidirect |
| 165. C4⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104731 | 2 |
| #23782139 | 2 |
| #23781670 | 2 |
| C2×#19104651 | 2 |
| #23781426 | 2 |
| #23781424 | 2 |
| #418×C163 | 2 |
| #1887 | 163 |