Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
578 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 578 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. #23782138 | C2 | semidirect |
| 3. C2×#19104649 | C2 | semidirect |
| 4. #23781520 | C2 | semidirect |
| 5. #23781520 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 12. #19104705 | C4 | semidirect |
| 33. C23×D163 | C2×C4 | semidirect |
| 45. C22×Dic163 | D4 | semidirect |
| 60. C22×C4×C163 | D4 | semidirect |
| 66. C22⋊C4×C163 | C2×C4 | semidirect |
| 87. C22×D163 | C22⋊C4 | semidirect |
| 99. C2×Dic163 | C22⋊C4 | semidirect |
| 160. C163 | #1889 | semidirect |
| 168. #342 | D163 | semidirect |
| 211. C22×C4 | D652 | semidirect |
| 226. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104705 | 2 |
| #23782138 | 2 |
| C2×#19104649 | 2 |
| #23781520 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #1889 | 163 |