Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23782073 | C2 | semidirect |
| 3. #23782071 | C2 | semidirect |
| 4. #23782069 | C2 | semidirect |
| 5. #23782067 | C2 | semidirect |
| 6. #23782066 | C2 | semidirect |
| 11. #500×C163 | C2 | semidirect |
| 42. #14579682 | Q8 | semidirect |
| 45. C8×D163 | Q8 | semidirect |
| 107. C163 | #3164 | semidirect |
| 113. #500 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782292 | 2 |
| #23782073 | 2 |
| #23782071 | 2 |
| #23782069 | 2 |
| #23782067 | 2 |
| #23782066 | 2 |
| #23781706 | 2 |
| #23781702 | 2 |
| #107×D163 | 2 |
| #23781619 | 2 |
| #500×C163 | 2 |
| #3164 | 163 |