Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19104755 | C2 | semidirect |
| 2. #23782215 | C2 | semidirect |
| 3. #23782047 | C2 | semidirect |
| 4. #23782044 | C2 | semidirect |
| 5. #23782041 | C2 | semidirect |
| 6. #23782039 | C2 | semidirect |
| 7. #23782037 | C2 | semidirect |
| 8. C2×C4×C163⋊C8 | C2 | semidirect |
| 9. #532×C163 | C2 | semidirect |
| 42. C2×C163⋊C8 | D4 | semidirect |
| 93. C4×C163 | #135 | semidirect |
| 101. C163 | #3147 | semidirect |
| 105. #532 | D163 | semidirect |
| 196. C4 | #19104755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104755 | 2 |
| #23782215 | 2 |
| #23782047 | 2 |
| #23782044 | 2 |
| #23782041 | 2 |
| #23782039 | 2 |
| #23782037 | 2 |
| C2×C4×C163⋊C8 | 2 |
| #532×C163 | 2 |
| #3147 | 163 |