Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×Q16×D163 | C2 | semidirect |
| 4. #23781823 | C2 | semidirect |
| 5. #23781822 | C2 | semidirect |
| 6. #23781821 | C2 | semidirect |
| 7. #23781820 | C2 | semidirect |
| 8. #23781819 | C2 | semidirect |
| 9. #103×D163 | C2 | semidirect |
| 11. #451×C163 | C2 | semidirect |
| 22. C2×Dic652 | C22 | semidirect |
| 23. C2×#14579689 | C22 | semidirect |
| 24. C2×#14579689 | C22 | semidirect |
| 35. #19104660 | C22 | semidirect |
| 36. #19104659 | C22 | semidirect |
| 37. #19104658 | C22 | semidirect |
| 41. C2×Q16×C163 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 99. C22×D163 | Q16 | semidirect |
| 140. C22×C163 | C2×Q16 | semidirect |
| 147. C2×D163 | C2×Q16 | semidirect |
| 164. D163 | #451 | direct (N × H) |
| 165. C163 | C2×#451 | semidirect |
| 175. #451 | D163 | direct (N × H) |
| 193. C2×Q16 | C2×D163 | semidirect |
| 207. #103 | C2×D163 | semidirect |
| 313. C22 | Q16×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D163 | 2 |
| C2×Q16×D163 | 2 |
| C22⋊Q8×D163 | 2 |
| #23781823 | 2 |
| #23781822 | 2 |
| #23781821 | 2 |
| #23781820 | 2 |
| #23781819 | 2 |
| #103×D163 | 2 |
| C22⋊C8×D163 | 2 |
| #451×C163 | 2 |
| C2×#451 | 163 |