Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23782011 | C2 | semidirect |
| 2. #23781945 | C2 | semidirect |
| 3. #23781870 | C2 | semidirect |
| 4. #23781409 | C2 | semidirect |
| 5. D4⋊(C163⋊C8) | C2 | semidirect |
| 6. D4⋊(C163⋊C8) | C2 | semidirect |
| 9. #19104735 | C22 | semidirect |
| 11. C4⋊(C163⋊C8) | C22 | semidirect |
| 12. C4⋊(C163⋊C8) | C22 | semidirect |
| 16. C4×C163⋊C8 | C22 | semidirect |
| 74. D4×C163 | SD16 | semidirect |
| 109. C163 | #1639 | semidirect |
| 180. D4 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782011 | 2 |
| #23781945 | 2 |
| #23781870 | 2 |
| #23781409 | 2 |
| D4⋊(C163⋊C8) | 2 |
| D42×C163 | 2 |
| #1639 | 163 |