Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #23782143 | C2 | semidirect |
| 4. #23781768 | C2 | semidirect |
| 5. #23781750 | C2 | semidirect |
| 6. #23781701 | C2 | semidirect |
| 8. #23781623 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 11. C2×#14579686 | C4 | semidirect |
| 16. Q8×Dic163 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104666 | C22 | semidirect |
| 26. #19104645 | C22 | semidirect |
| 27. C8×Dic163 | C22 | semidirect |
| 31. #103×C163 | C22 | semidirect |
| 38. #14579686 | C2×C4 | semidirect |
| 39. #14579686 | C2×C4 | semidirect |
| 40. C2×C163⋊C8 | C2×C4 | semidirect |
| 54. C2×Q8×C163 | C2×C4 | semidirect |
| 103. C163 | #2949 | semidirect |
| 111. #419 | D163 | semidirect |
| 132. #103 | C2×D163 | semidirect |
| 139. C2×Q8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| #23782143 | 2 |
| #23782139 | 2 |
| #23781768 | 2 |
| #23781750 | 2 |
| #23781701 | 2 |
| #23781671 | 2 |
| #23781623 | 2 |
| #419×C163 | 2 |
| #2949 | 163 |