Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #23782075 | C2 | semidirect |
| 4. #23782074 | C2 | semidirect |
| 5. #23782071 | C2 | semidirect |
| 6. #23782069 | C2 | semidirect |
| 7. #23782062 | C2 | semidirect |
| 11. #501×C163 | C2 | semidirect |
| 52. #14579682 | Q8 | semidirect |
| 95. C163⋊C8 | C2×Q8 | semidirect |
| 103. C8×C163 | C2×Q8 | semidirect |
| 124. C163 | #3165 | semidirect |
| 131. #501 | D163 | semidirect |
| 228. C8 | Q8×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782221 | 2 |
| C4⋊Q8×D163 | 2 |
| #23782075 | 2 |
| #23782074 | 2 |
| #23782071 | 2 |
| #23782069 | 2 |
| #23782062 | 2 |
| #23781706 | 2 |
| #23781704 | 2 |
| #23781617 | 2 |
| #501×C163 | 2 |
| #3165 | 163 |