Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
754 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19104766 | C2 | semidirect |
| 3. #23781825 | C2 | semidirect |
| 4. #23781820 | C2 | semidirect |
| 5. #23781815 | C2 | semidirect |
| 6. #23781664 | C2 | semidirect |
| 7. #23781629 | C2 | semidirect |
| 8. C2×C22⋊Q8×C163 | C2 | semidirect |
| 19. C2×#14579689 | C22 | semidirect |
| 20. C2×#14579686 | C22 | semidirect |
| 21. C2×#14579683 | C22 | semidirect |
| 22. #19104658 | C22 | semidirect |
| 23. #19104655 | C22 | semidirect |
| 25. C22⋊(C163⋊C8) | C22 | semidirect |
| 26. C22×Q8×C163 | C22 | semidirect |
| 31. C22⋊Q8×C163 | C22 | semidirect |
| 33. C2×C4⋊C4×C163 | C22 | semidirect |
| 126. C22×C163 | #137 | semidirect |
| 146. C163 | #3007 | semidirect |
| 150. C2×C22⋊Q8 | D163 | semidirect |
| 162. C22×Q8 | C2×D163 | semidirect |
| 174. C22⋊Q8 | C2×D163 | semidirect |
| 176. C2×C4⋊C4 | C2×D163 | semidirect |
| 277. C22 | #19104766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104766 | 2 |
| #23781825 | 2 |
| #23781820 | 2 |
| #23781815 | 2 |
| #23781664 | 2 |
| #23781629 | 2 |
| C2×C22⋊Q8×C163 | 2 |
| #3007 | 163 |