Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #23782385 | C2 | semidirect |
| 3. #23782070 | C2 | semidirect |
| 4. #23782001 | C2 | semidirect |
| 5. #23781990 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 7. #23781946 | C2 | semidirect |
| 8. #23781911 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 10. #23781707 | C2 | semidirect |
| 11. #436×C163 | C2 | semidirect |
| 99. C8×C163 | #41 | semidirect |
| 122. C163 | #3353 | semidirect |
| 133. #436 | D163 | semidirect |
| 222. C8 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782385 | 2 |
| #23782319 | 2 |
| #23782070 | 2 |
| #23782001 | 2 |
| #23781990 | 2 |
| #23781951 | 2 |
| #23781946 | 2 |
| #23781911 | 2 |
| C4×#14579688 | 2 |
| #23781707 | 2 |
| #436×C163 | 2 |
| #3353 | 163 |