Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23782319 | C2 | semidirect |
| 2. #23782011 | C2 | semidirect |
| 3. #23781857 | C2 | semidirect |
| 4. #23781412 | C2 | semidirect |
| 5. D4⋊(C163⋊C8) | C2 | semidirect |
| 6. #23781392 | C2 | semidirect |
| 7. #459×C163 | C2 | semidirect |
| 72. D4×C163 | D8 | semidirect |
| 104. C163 | #1625 | semidirect |
| 109. #459 | D163 | semidirect |
| 170. D4 | #14579684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782319 | 2 |
| #23782011 | 2 |
| #23781857 | 2 |
| #23781412 | 2 |
| D4⋊(C163⋊C8) | 2 |
| #23781392 | 2 |
| #459×C163 | 2 |
| #1625 | 163 |