Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782239 | C2 | semidirect |
| 4. #23781846 | C2 | semidirect |
| 5. #23781841 | C2 | semidirect |
| 6. #23781682 | C2 | semidirect |
| 7. #23781681 | C2 | semidirect |
| 8. #23781647 | C2 | semidirect |
| 9. C2×#137×C163 | C2 | semidirect |
| 23. #19104766 | C22 | semidirect |
| 26. C2×#14579683 | C22 | semidirect |
| 27. #19104733 | C22 | semidirect |
| 28. #19104724 | C22 | semidirect |
| 31. #19104694 | C22 | semidirect |
| 32. #19104662 | C22 | semidirect |
| 33. #19104661 | C22 | semidirect |
| 34. #19104653 | C22 | semidirect |
| 35. #19104651 | C22 | semidirect |
| 37. C22×Q8×C163 | C22 | semidirect |
| 39. #137×C163 | C22 | semidirect |
| 42. C2×M16×C163 | C22 | semidirect |
| 192. C163 | #3022 | semidirect |
| 196. C2×#137 | D163 | semidirect |
| 216. C22×Q8 | C2×D163 | semidirect |
| 220. #137 | C2×D163 | semidirect |
| 226. C2×M16 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104766 | 2 |
| #23782239 | 2 |
| #23781846 | 2 |
| #23781841 | 2 |
| #23781682 | 2 |
| #23781681 | 2 |
| #23781647 | 2 |
| C2×#137×C163 | 2 |
| #3022 | 163 |