Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
382 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782142 | C2 | semidirect |
| 3. #23781990 | C2 | semidirect |
| 4. #23781973 | C2 | semidirect |
| 5. #23781866 | C2 | semidirect |
| 6. #23781806 | C2 | semidirect |
| 7. #23781767 | C2 | semidirect |
| 8. C4×#14579688 | C2 | semidirect |
| 9. #433×C163 | C2 | semidirect |
| 101. C163 | #3126 | semidirect |
| 111. #433 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23782142 | 2 |
| #23781990 | 2 |
| #23781973 | 2 |
| #23781866 | 2 |
| #23781806 | 2 |
| #23781767 | 2 |
| C4×#14579688 | 2 |
| #433×C163 | 2 |
| #3126 | 163 |