Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 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 |
|---|---|---|
| 2. C22×#14579689 | C2 | semidirect |
| 3. #23782142 | C2 | semidirect |
| 4. #23781884 | C2 | semidirect |
| 5. #23781872 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781674 | C2 | semidirect |
| 111. C163 | #3044 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C22×#14579689 | 2 |
| #23782142 | 2 |
| #23781884 | 2 |
| #23781872 | 2 |
| #23781692 | 2 |
| #23781674 | 2 |
| #23781661 | 2 |
| #536×C163 | 2 |
| #3044 | 163 |