Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
500 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×M16×D163 | C2 | semidirect |
| 3. #23782178 | C2 | semidirect |
| 4. #23781920 | C2 | semidirect |
| 5. #23781919 | C2 | semidirect |
| 6. #23781918 | C2 | semidirect |
| 7. #23781914 | C2 | semidirect |
| 8. #23781913 | C2 | semidirect |
| 9. #23781700 | C2 | semidirect |
| 10. #23781660 | C2 | semidirect |
| 11. #470×C163 | C2 | semidirect |
| 15. C2×#14579686 | C22 | semidirect |
| 16. C2×D1304 | C22 | semidirect |
| 31. #19104668 | C22 | semidirect |
| 32. #19104667 | C22 | semidirect |
| 33. #19104659 | C22 | semidirect |
| 34. #19104657 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 36. C2×Q16×C163 | C22 | semidirect |
| 39. #106×C163 | C22 | semidirect |
| 40. #103×C163 | C22 | semidirect |
| 64. C8×D163 | D4 | semidirect |
| 140. C163 | #3054 | semidirect |
| 146. #470 | D163 | semidirect |
| 156. C2×Q16 | C2×D163 | semidirect |
| 177. #106 | C2×D163 | semidirect |
| 179. #103 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×M16×D163 | 2 |
| #23782178 | 2 |
| #23781920 | 2 |
| #23781919 | 2 |
| #23781918 | 2 |
| #23781914 | 2 |
| #23781913 | 2 |
| #23781700 | 2 |
| #23781660 | 2 |
| #470×C163 | 2 |
| #3054 | 163 |