Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
480 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 157 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×#19104735 | C2 | semidirect |
| 3. #23781875 | C2 | semidirect |
| 4. #23781870 | C2 | semidirect |
| 5. #23781689 | C2 | semidirect |
| 6. #23781673 | C2 | semidirect |
| 89. C4×C163 | #137 | semidirect |
| 97. C163 | #3039 | semidirect |
| 188. C4 | #19104765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C2×#19104735 | 2 |
| #23781875 | 2 |
| #23781870 | 2 |
| #23781689 | 2 |
| #23781673 | 2 |
| C4×#41×C163 | 2 |
| #3039 | 163 |