Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19104758 | C2 | semidirect |
| 2. C22×C8×D163 | C2 | semidirect |
| 3. #23782178 | C2 | semidirect |
| 4. #23781903 | C2 | semidirect |
| 5. #23781902 | C2 | semidirect |
| 6. #23781901 | C2 | semidirect |
| 7. #23781897 | C2 | semidirect |
| 8. #23781896 | C2 | semidirect |
| 9. #23781702 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. #467×C163 | C2 | semidirect |
| 15. C2×#14579686 | C22 | semidirect |
| 16. C2×D1304 | C22 | semidirect |
| 31. #19104669 | C22 | semidirect |
| 32. #19104666 | C22 | semidirect |
| 33. #19104659 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 36. C2×Q16×C163 | C22 | semidirect |
| 39. #107×C163 | C22 | semidirect |
| 40. #103×C163 | C22 | semidirect |
| 64. C8×D163 | D4 | semidirect |
| 118. C22×C163 | #135 | semidirect |
| 129. C2×D163 | #135 | semidirect |
| 145. C163 | #3050 | semidirect |
| 151. #467 | D163 | semidirect |
| 161. C2×Q16 | C2×D163 | semidirect |
| 181. #107 | C2×D163 | semidirect |
| 184. #103 | C2×D163 | semidirect |
| 274. C22 | #19104758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C22×C8×D163 | 2 |
| #23782178 | 2 |
| #23781903 | 2 |
| #23781902 | 2 |
| #23781901 | 2 |
| #23781897 | 2 |
| #23781896 | 2 |
| #23781702 | 2 |
| #23781660 | 2 |
| #467×C163 | 2 |
| #3050 | 163 |