Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782027 | C2 | semidirect |
| 3. #23782022 | C2 | semidirect |
| 4. #23781673 | C2 | semidirect |
| 6. C4×#14579683 | C2 | semidirect |
| 7. #533×C163 | C2 | semidirect |
| 15. #19104658 | C22 | semidirect |
| 17. #19104646 | C22 | semidirect |
| 18. C4×C163⋊C8 | C22 | semidirect |
| 19. C4⋊Q8×C163 | C22 | semidirect |
| 20. #125×C163 | C22 | semidirect |
| 83. C163 | #3140 | semidirect |
| 85. #533 | D163 | semidirect |
| 95. C4⋊Q8 | C2×D163 | semidirect |
| 96. #125 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104723 | 2 |
| #23782027 | 2 |
| #23782022 | 2 |
| #23781673 | 2 |
| #23781669 | 2 |
| C4×#14579683 | 2 |
| #533×C163 | 2 |
| #3140 | 163 |