Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104756 | C2 | semidirect |
| 3. C2×#19104754 | C2 | semidirect |
| 4. #23782214 | C2 | semidirect |
| 5. #23782049 | C2 | semidirect |
| 6. #23782047 | C2 | semidirect |
| 7. #23782043 | C2 | semidirect |
| 8. #23782040 | C2 | semidirect |
| 9. #23782036 | C2 | semidirect |
| 10. C4×C8×D163 | C2 | semidirect |
| 11. #495×C163 | C2 | semidirect |
| 62. C8×D163 | D4 | semidirect |
| 63. C8×D163 | D4 | semidirect |
| 119. Dic163 | #135 | semidirect |
| 125. C163 | #3147 | semidirect |
| 133. #495 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×#19104756 | 2 |
| C2×#19104754 | 2 |
| #23782214 | 2 |
| #23782049 | 2 |
| #23782047 | 2 |
| #23782043 | 2 |
| #23782040 | 2 |
| #23782036 | 2 |
| C4×C8×D163 | 2 |
| #495×C163 | 2 |
| #3147 | 163 |