Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782222 | C2 | semidirect |
| 2. #23781995 | C2 | semidirect |
| 3. #23781955 | C2 | semidirect |
| 4. #23781870 | C2 | semidirect |
| 6. C4×#14579687 | C2 | semidirect |
| 7. #23781718 | C2 | semidirect |
| 10. #19104735 | C22 | semidirect |
| 11. #19104735 | C22 | semidirect |
| 16. C4×Dic326 | C22 | semidirect |
| 18. #19104666 | C22 | semidirect |
| 19. C4⋊(C163⋊C8) | C22 | semidirect |
| 20. #19104658 | C22 | semidirect |
| 23. C4×C163⋊C8 | C22 | semidirect |
| 83. C2×C4×C163 | SD16 | semidirect |
| 112. C163 | #3101 | semidirect |
| 195. C2×C4 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23781995 | 2 |
| #23781955 | 2 |
| #23781870 | 2 |
| #23781816 | 2 |
| C4×#14579687 | 2 |
| #23781718 | 2 |
| C2×C4×D4×C163 | 2 |
| #3101 | 163 |