Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 3. #23781952 | C2 | semidirect |
| 4. #23781947 | C2 | semidirect |
| 5. #23781942 | C2 | semidirect |
| 6. #23781705 | C2 | semidirect |
| 7. #23781689 | C2 | semidirect |
| 9. C2×C4⋊Q8×C163 | C2 | semidirect |
| 36. #14579699 | Q8 | semidirect |
| 72. Dic326 | C2×Q8 | semidirect |
| 74. D652 | C2×Q8 | semidirect |
| 121. C163 | #3079 | semidirect |
| 123. C2×C4⋊Q8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579699 | 2 |
| #23781957 | 2 |
| #23781952 | 2 |
| #23781947 | 2 |
| #23781942 | 2 |
| #23781705 | 2 |
| #23781689 | 2 |
| #23781664 | 2 |
| C2×C4⋊Q8×C163 | 2 |
| #3079 | 163 |