Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. D4×Dic326 | C2 | semidirect |
| 2. #23782012 | C2 | semidirect |
| 3. #23781866 | C2 | semidirect |
| 5. #23781412 | C2 | semidirect |
| 6. #23781397 | C2 | semidirect |
| 7. D4⋊C8×C163 | C2 | semidirect |
| 56. Dic326 | D8 | semidirect |
| 69. D4×C163 | SD16 | semidirect |
| 99. C163 | #1627 | semidirect |
| 107. D4⋊C8 | D163 | semidirect |
| 164. D4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic326 | 2 |
| #23782012 | 2 |
| #23781866 | 2 |
| #23781860 | 2 |
| #23781412 | 2 |
| #23781397 | 2 |
| D4⋊C8×C163 | 2 |
| #1627 | 163 |