Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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. #23782463 | C2 | semidirect |
| 2. #23782176 | C2 | semidirect |
| 3. #23781683 | C2 | semidirect |
| 4. #23781682 | C2 | semidirect |
| 5. #23781629 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. #525×C163 | C2 | semidirect |
| 37. C2×Dic326 | D4 | semidirect |
| 38. C2×D652 | D4 | semidirect |
| 51. C2×C163⋊C8 | D4 | semidirect |
| 57. C4×Dic163 | D4 | semidirect |
| 63. C2×Q8×C163 | D4 | semidirect |
| 66. C2×D4×C163 | D4 | semidirect |
| 81. C42×C163 | D4 | semidirect |
| 157. C163 | #2010 | semidirect |
| 161. #525 | D163 | semidirect |
| 201. C2×Q8 | C22⋊D163 | semidirect |
| 207. C2×D4 | C22⋊D163 | semidirect |
| 239. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23782176 | 2 |
| #23781683 | 2 |
| #23781682 | 2 |
| #23781629 | 2 |
| #23781421 | 2 |
| #525×C163 | 2 |
| #2010 | 163 |