Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23782017 | C2 | semidirect |
| 3. #23781867 | C2 | semidirect |
| 4. #23781413 | C2 | semidirect |
| 5. D4⋊(C163⋊C8) | C2 | semidirect |
| 6. #23781392 | C2 | semidirect |
| 7. #474×C163 | C2 | semidirect |
| 93. C163 | #1646 | semidirect |
| 97. #474 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782017 | 2 |
| #23781867 | 2 |
| #23781413 | 2 |
| D4⋊(C163⋊C8) | 2 |
| #23781392 | 2 |
| #474×C163 | 2 |
| #1646 | 163 |