Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23781783 | C2 | semidirect |
| 3. #23781494 | C2 | semidirect |
| 4. #23781472 | C2 | semidirect |
| 5. #23781471 | C2 | semidirect |
| 6. C4×C163⋊C16 | C2 | semidirect |
| 7. #443×C163 | C2 | semidirect |
| 10. #19104681 | C4 | semidirect |
| 11. #19104679 | C4 | semidirect |
| 12. #19104678 | C4 | semidirect |
| 13. #19104676 | C4 | semidirect |
| 71. C163 | #2178 | semidirect |
| 75. #443 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782095 | 2 |
| #23781783 | 2 |
| #23781494 | 2 |
| #23781472 | 2 |
| #23781471 | 2 |
| C4×C163⋊C16 | 2 |
| #443×C163 | 2 |
| #2178 | 163 |