Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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×#19104758 | C2 | semidirect |
| 2. #23782337 | C2 | semidirect |
| 3. #23782318 | C2 | semidirect |
| 4. #23782039 | C2 | semidirect |
| 5. #23781897 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781826 | C2 | semidirect |
| 8. #23781813 | C2 | semidirect |
| 9. C4×#14579686 | C2 | semidirect |
| 10. #23781730 | C2 | semidirect |
| 11. #462×C163 | C2 | semidirect |
| 60. #14579686 | D4 | semidirect |
| 129. C4×C163 | #135 | semidirect |
| 140. C163 | #3284 | semidirect |
| 147. #462 | D163 | semidirect |
| 272. C4 | #19104758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| #23782337 | 2 |
| #23782318 | 2 |
| #23782039 | 2 |
| #23781897 | 2 |
| #23781861 | 2 |
| #23781826 | 2 |
| #23781813 | 2 |
| C4×#14579686 | 2 |
| #23781730 | 2 |
| #462×C163 | 2 |
| #3284 | 163 |