Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23781717 | C2 | semidirect |
| 3. #23781414 | C2 | semidirect |
| 4. #23781408 | C2 | semidirect |
| 5. #333×C163 | C2 | semidirect |
| 65. C163 | #1543 | semidirect |
| 70. #333 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| #23781717 | 2 |
| #23781414 | 2 |
| #23781408 | 2 |
| #333×C163 | 2 |
| #1543 | 163 |