Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×Q16×D163 | C2 | semidirect |
| 3. #23782327 | C2 | semidirect |
| 4. #23782049 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 6. #23781902 | C2 | semidirect |
| 7. #23781887 | C2 | semidirect |
| 8. #23781830 | C2 | semidirect |
| 9. #23781805 | C2 | semidirect |
| 10. C8×D652 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 73. Q16×C163 | D4 | semidirect |
| 120. C2×D163 | #135 | semidirect |
| 136. C163 | #3285 | semidirect |
| 147. C4×Q16 | D163 | semidirect |
| 195. Q16 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×Q16×D163 | 2 |
| #23782327 | 2 |
| #23782049 | 2 |
| #23781907 | 2 |
| #23781902 | 2 |
| #23781887 | 2 |
| #23781830 | 2 |
| #23781805 | 2 |
| C8×D652 | 2 |
| C4×Q16×C163 | 2 |
| #3285 | 163 |