Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782293 | C2 | semidirect |
| 3. #23781971 | C2 | semidirect |
| 4. #23781968 | C2 | semidirect |
| 5. #23781954 | C2 | semidirect |
| 6. #23781949 | C2 | semidirect |
| 7. C2×#19104666 | C2 | semidirect |
| 8. #23781693 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 42. #14579699 | Q8 | semidirect |
| 123. C163 | #3084 | semidirect |
| 131. #428 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782146 | 2 |
| #23781971 | 2 |
| #23781968 | 2 |
| #23781954 | 2 |
| #23781949 | 2 |
| C2×#19104666 | 2 |
| #23781693 | 2 |
| #23781667 | 2 |
| #23781659 | 2 |
| #428×C163 | 2 |
| #3084 | 163 |