Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. #23781487 | C2 | semidirect |
| 4. #23781482 | C2 | semidirect |
| 5. #23781480 | C2 | semidirect |
| 7. #365×C163 | C2 | semidirect |
| 61. C163 | #2239 | semidirect |
| 66. #365 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781924 | 2 |
| #23781712 | 2 |
| #23781487 | 2 |
| #23781482 | 2 |
| #23781480 | 2 |
| #23781446 | 2 |
| #365×C163 | 2 |
| #2239 | 163 |