Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23781974 | C2 | semidirect |
| 4. #23781970 | C2 | semidirect |
| 5. #23781958 | C2 | semidirect |
| 6. #23781948 | C2 | semidirect |
| 72. C2×Q8×C163 | Q8 | semidirect |
| 129. C163 | #3078 | semidirect |
| 177. C2×Q8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| C2×Q8×Dic163 | 2 |
| #23781974 | 2 |
| #23781970 | 2 |
| #23781958 | 2 |
| #23781948 | 2 |
| #23781708 | 2 |
| #23781707 | 2 |
| #23781688 | 2 |
| #23781674 | 2 |
| #419×C163 | 2 |
| #3078 | 163 |