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. #23782252 | C2 | semidirect |
| 2. #23781818 | C2 | semidirect |
| 3. #23781798 | C2 | semidirect |
| 4. #23781575 | C2 | semidirect |
| 5. #23781401 | C2 | semidirect |
| 6. #23781388 | C2 | semidirect |
| 7. #327×C163 | C2 | semidirect |
| 29. C2×Dic326 | D4 | semidirect |
| 44. C4⋊Dic163 | D4 | semidirect |
| 55. C2×D4×C163 | D4 | semidirect |
| 59. C4⋊C4×C163 | D4 | semidirect |
| 135. C163 | #1600 | semidirect |
| 142. #327 | D163 | semidirect |
| 175. C2×D4 | D652 | semidirect |
| 187. C4⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782252 | 2 |
| #23781818 | 2 |
| #23781798 | 2 |
| #23781575 | 2 |
| #23781401 | 2 |
| #23781388 | 2 |
| #327×C163 | 2 |
| #1600 | 163 |