Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #23781773 | C2 | semidirect |
| 4. #23781772 | C2 | semidirect |
| 5. #23781771 | C2 | semidirect |
| 6. C4×#14579689 | C2 | semidirect |
| 7. #23781757 | C2 | semidirect |
| 11. #441×C163 | C2 | semidirect |
| 15. Q16×D163 | C4 | semidirect |
| 108. C163 | #2950 | semidirect |
| 115. #441 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D163 | 2 |
| #23782141 | 2 |
| #23781773 | 2 |
| #23781772 | 2 |
| #23781771 | 2 |
| C4×#14579689 | 2 |
| #23781757 | 2 |
| #23781700 | 2 |
| #23781672 | 2 |
| #23781622 | 2 |
| #441×C163 | 2 |
| #2950 | 163 |