Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 149 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. #23782073 | C2 | semidirect |
| 3. #23782072 | C2 | semidirect |
| 27. C2×C163⋊C8 | Q8 | semidirect |
| 38. C2×C8×C163 | Q8 | semidirect |
| 69. C163 | #3162 | semidirect |
| 100. C2×C8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| #23782073 | 2 |
| #23782072 | 2 |
| #23781703 | 2 |
| #23781701 | 2 |
| C2×#19104645 | 2 |
| #427×C163 | 2 |
| #3162 | 163 |