Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
700 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 1. C2×#19104765 | C2 | semidirect |
| 2. C22×#14579689 | C2 | semidirect |
| 3. #23782236 | C2 | semidirect |
| 4. #23781827 | C2 | semidirect |
| 5. #23781821 | C2 | semidirect |
| 6. #23781674 | C2 | semidirect |
| 7. #23781661 | C2 | semidirect |
| 8. #23781632 | C2 | semidirect |
| 140. C163 | #3011 | 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 |
| #23782236 | 2 |
| #23781827 | 2 |
| #23781821 | 2 |
| #23781674 | 2 |
| #23781661 | 2 |
| #23781632 | 2 |
| C2×2−1+4×C163 | 2 |
| #3011 | 163 |