Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 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. #23781865 | C2 | semidirect |
| 3. #23781796 | C2 | semidirect |
| 4. #23781415 | C2 | semidirect |
| 5. #23781409 | C2 | semidirect |
| 6. #23781408 | C2 | semidirect |
| 7. #460×C163 | C2 | semidirect |
| 52. C163⋊C8 | SD16 | semidirect |
| 86. C163 | #1688 | semidirect |
| 90. #460 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782041 | 2 |
| #23781865 | 2 |
| #23781796 | 2 |
| #23781415 | 2 |
| #23781409 | 2 |
| #23781408 | 2 |
| #460×C163 | 2 |
| #1688 | 163 |