Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782372 | C2 | semidirect |
| 2. #23782336 | C2 | semidirect |
| 3. #23782028 | C2 | semidirect |
| 4. #23782012 | C2 | semidirect |
| 5. #23781968 | C2 | semidirect |
| 6. #23781955 | C2 | semidirect |
| 7. #23781860 | C2 | semidirect |
| 8. #23781858 | C2 | semidirect |
| 9. #23781795 | C2 | semidirect |
| 10. #23781774 | C2 | semidirect |
| 11. C4×D8×C163 | C2 | semidirect |
| 94. D4×C163 | #41 | semidirect |
| 129. C163 | #3366 | semidirect |
| 141. C4×D8 | D163 | semidirect |
| 218. D4 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782372 | 2 |
| #23782336 | 2 |
| #23782028 | 2 |
| #23782012 | 2 |
| #23781968 | 2 |
| #23781955 | 2 |
| #23781860 | 2 |
| #23781858 | 2 |
| #23781795 | 2 |
| #23781774 | 2 |
| C4×D8×C163 | 2 |
| #3366 | 163 |