Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782011 | C2 | semidirect |
| 3. #23781946 | C2 | semidirect |
| 4. #23781876 | C2 | semidirect |
| 5. #23781395 | C2 | semidirect |
| 6. #23781392 | C2 | semidirect |
| 7. #331×C163 | C2 | semidirect |
| 99. C163 | #1641 | semidirect |
| 105. #331 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782335 | 2 |
| #23782011 | 2 |
| #23781946 | 2 |
| #23781876 | 2 |
| #23781395 | 2 |
| #23781392 | 2 |
| #331×C163 | 2 |
| #1641 | 163 |