Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104783 | C2 | semidirect |
| 2. C2×#19104755 | C2 | semidirect |
| 3. #23782243 | C2 | semidirect |
| 4. #23781826 | C2 | semidirect |
| 5. #23781819 | C2 | semidirect |
| 6. #23781809 | C2 | semidirect |
| 7. #23781802 | C2 | semidirect |
| 8. #23781667 | C2 | semidirect |
| 9. C2×#19104659 | C2 | semidirect |
| 10. #23781633 | C2 | semidirect |
| 11. C2×#137×C163 | C2 | semidirect |
| 52. #14579699 | D4 | semidirect |
| 86. C2×Q8×C163 | D4 | semidirect |
| 169. C163 | #3013 | semidirect |
| 172. C2×#137 | D163 | semidirect |
| 233. C2×Q8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| C2×#19104755 | 2 |
| #23782243 | 2 |
| #23781826 | 2 |
| #23781819 | 2 |
| #23781809 | 2 |
| #23781802 | 2 |
| #23781667 | 2 |
| C2×#19104659 | 2 |
| #23781633 | 2 |
| C2×#137×C163 | 2 |
| #3013 | 163 |