Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781957 | C2 | semidirect |
| 4. #23781411 | C2 | semidirect |
| 5. #23781397 | C2 | semidirect |
| 7. #487×C163 | C2 | semidirect |
| 86. C163 | #1638 | semidirect |
| 89. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782389 | 2 |
| #23781957 | 2 |
| #23781952 | 2 |
| #23781411 | 2 |
| #23781397 | 2 |
| #23781394 | 2 |
| #487×C163 | 2 |
| #1638 | 163 |