Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
384 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 5. #23781958 | C2 | semidirect |
| 6. #23781873 | C2 | semidirect |
| 8. Q16×Dic163 | C2 | semidirect |
| 9. #23781757 | C2 | semidirect |
| 88. C2×Dic163 | Q16 | semidirect |
| 127. C163 | #3104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782217 | 2 |
| C2×Q8×Dic163 | 2 |
| #23782001 | 2 |
| #23781998 | 2 |
| #23781958 | 2 |
| #23781873 | 2 |
| #23781821 | 2 |
| Q16×Dic163 | 2 |
| #23781757 | 2 |
| #23781715 | 2 |
| #451×C163 | 2 |
| #3104 | 163 |