Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#19104757 | C2 | semidirect |
| 2. C2×#19104755 | C2 | semidirect |
| 3. #23782211 | C2 | semidirect |
| 4. #23782050 | C2 | semidirect |
| 5. #23782048 | C2 | semidirect |
| 6. #23782046 | C2 | semidirect |
| 7. #23782043 | C2 | semidirect |
| 8. #23782040 | C2 | semidirect |
| 9. #23782036 | C2 | semidirect |
| 10. C2×C8×Dic163 | C2 | semidirect |
| 11. C2×#135×C163 | C2 | semidirect |
| 55. C2×C163⋊C8 | D4 | semidirect |
| 74. C2×C8×C163 | D4 | semidirect |
| 119. Dic163 | #135 | semidirect |
| 125. C163 | #3147 | semidirect |
| 129. C2×#135 | D163 | semidirect |
| 194. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104757 | 2 |
| C2×#19104755 | 2 |
| #23782211 | 2 |
| #23782050 | 2 |
| #23782048 | 2 |
| #23782046 | 2 |
| #23782043 | 2 |
| #23782040 | 2 |
| #23782036 | 2 |
| C2×C8×Dic163 | 2 |
| C2×#135×C163 | 2 |
| #3147 | 163 |