Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23782224 | C2 | semidirect |
| 2. C2×#19104705 | C2 | semidirect |
| 3. C2×#19104703 | C2 | semidirect |
| 4. C2×#19104649 | C2 | semidirect |
| 5. #23781520 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. C2×#99×C163 | C2 | semidirect |
| 38. C23×D163 | D4 | semidirect |
| 39. C23×D163 | D4 | semidirect |
| 52. C22×Dic163 | D4 | semidirect |
| 53. C22×Dic163 | D4 | semidirect |
| 59. C22⋊Dic163 | D4 | semidirect |
| 64. C24×C163 | D4 | semidirect |
| 74. C22×C4×C163 | D4 | semidirect |
| 78. C22⋊C4×C163 | D4 | semidirect |
| 187. C163 | #2021 | semidirect |
| 193. C2×#99 | D163 | semidirect |
| 228. C24 | D652 | semidirect |
| 252. C22×C4 | D652 | semidirect |
| 266. C22⋊C4 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782224 | 2 |
| C2×#19104705 | 2 |
| C2×#19104703 | 2 |
| C2×#19104649 | 2 |
| #23781520 | 2 |
| #23781431 | 2 |
| C2×#99×C163 | 2 |
| #2021 | 163 |