Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 2. #23781972 | C2 | semidirect |
| 3. #23781960 | C2 | semidirect |
| 4. #23781950 | C2 | semidirect |
| 47. C2×Q8×C163 | Q8 | semidirect |
| 106. C163 | #3078 | semidirect |
| 144. C2×Q8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23781972 | 2 |
| #23781960 | 2 |
| #23781950 | 2 |
| #23781705 | 2 |
| #23781689 | 2 |
| #23781674 | 2 |
| C2×C4×Q8×C163 | 2 |
| #3078 | 163 |