Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19104733 | C2 | semidirect |
| 4. #23781674 | C2 | semidirect |
| 5. C2×#19104653 | C2 | semidirect |
| 6. #23781426 | C2 | semidirect |
| 125. C163 | #2005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782236 | 2 |
| C2×#19104733 | 2 |
| C2×#19104662 | 2 |
| #23781674 | 2 |
| C2×#19104653 | 2 |
| #23781426 | 2 |
| C2×#137×C163 | 2 |
| #2005 | 163 |