Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19104756 | C2 | semidirect |
| 2. #23782319 | C2 | semidirect |
| 3. #23782318 | C2 | semidirect |
| 4. #23782044 | C2 | semidirect |
| 5. #23781905 | C2 | semidirect |
| 6. #23781871 | C2 | semidirect |
| 7. #23781830 | C2 | semidirect |
| 8. #23781824 | C2 | semidirect |
| 9. C4×#14579684 | C2 | semidirect |
| 10. #23781730 | C2 | semidirect |
| 11. #461×C163 | C2 | semidirect |
| 58. #14579684 | D4 | semidirect |
| 126. C4×C163 | #135 | semidirect |
| 138. C163 | #3283 | semidirect |
| 146. #461 | D163 | semidirect |
| 268. C4 | #19104756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104756 | 2 |
| #23782319 | 2 |
| #23782318 | 2 |
| #23782044 | 2 |
| #23781905 | 2 |
| #23781871 | 2 |
| #23781830 | 2 |
| #23781824 | 2 |
| C4×#14579684 | 2 |
| #23781730 | 2 |
| #461×C163 | 2 |
| #3283 | 163 |