Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
260 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782402 | C2 | semidirect |
| 2. #23781856 | C2 | semidirect |
| 3. #23781853 | C2 | semidirect |
| 4. #23781832 | C2 | semidirect |
| 5. #23781454 | C2 | semidirect |
| 6. #23781451 | C2 | semidirect |
| 7. #353×C163 | C2 | semidirect |
| 38. C22×Dic163 | D4 | semidirect |
| 49. C22⋊Dic163 | D4 | semidirect |
| 57. C2×D4×C163 | D4 | semidirect |
| 61. C42×C163 | D4 | semidirect |
| 127. C163 | #2200 | semidirect |
| 133. #353 | D163 | semidirect |
| 167. C2×D4 | D652 | semidirect |
| 189. C42 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782402 | 2 |
| #23781856 | 2 |
| #23781853 | 2 |
| #23781832 | 2 |
| #23781454 | 2 |
| #23781451 | 2 |
| #353×C163 | 2 |
| #2200 | 163 |