Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 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×#19104767 | C2 | semidirect |
| 2. C2×#19104764 | C2 | semidirect |
| 4. C4⋊Q8×D163 | C2 | semidirect |
| 5. #23782060 | C2 | semidirect |
| 6. #23782059 | C2 | semidirect |
| 7. #23782057 | C2 | semidirect |
| 8. #23782043 | C2 | semidirect |
| 9. #23782036 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #497×C163 | C2 | semidirect |
| 63. #14579682 | D4 | semidirect |
| 124. Dic163 | #137 | semidirect |
| 130. C163 | #3152 | semidirect |
| 139. #497 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104767 | 2 |
| C2×#19104764 | 2 |
| #23782214 | 2 |
| C4⋊Q8×D163 | 2 |
| #23782060 | 2 |
| #23782059 | 2 |
| #23782057 | 2 |
| #23782043 | 2 |
| #23782036 | 2 |
| #23781617 | 2 |
| #497×C163 | 2 |
| #3152 | 163 |