Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23781460 | C2 | semidirect |
| 4. #23781459 | C2 | semidirect |
| 5. #354×C163 | C2 | semidirect |
| 7. C2×Q8×D163 | C4 | semidirect |
| 8. #19104735 | C4 | semidirect |
| 9. #19104733 | C4 | semidirect |
| 13. #19104692 | C4 | semidirect |
| 81. C163 | #2129 | semidirect |
| 87. #354 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782235 | 2 |
| #23781637 | 2 |
| #23781460 | 2 |
| #23781459 | 2 |
| #354×C163 | 2 |
| #2129 | 163 |