Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
| 3. #23781996 | C2 | semidirect |
| 4. #23781956 | C2 | semidirect |
| 5. #23781871 | C2 | semidirect |
| 7. C4×#14579688 | C2 | semidirect |
| 8. #431×C163 | C2 | semidirect |
| 12. #19104735 | C22 | semidirect |
| 13. #19104735 | C22 | semidirect |
| 18. C4×Dic326 | C22 | semidirect |
| 26. #19104667 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 30. C4⋊C8×C163 | C22 | semidirect |
| 32. C4×C8×C163 | C22 | semidirect |
| 82. C2×C4×C163 | SD16 | semidirect |
| 112. C163 | #3101 | semidirect |
| 121. #431 | D163 | semidirect |
| 141. C4⋊C8 | C2×D163 | semidirect |
| 145. C4×C8 | C2×D163 | semidirect |
| 195. C2×C4 | #14579688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| C2×C4×D652 | 2 |
| #23781996 | 2 |
| #23781956 | 2 |
| #23781871 | 2 |
| #23781818 | 2 |
| C4×#14579688 | 2 |
| #431×C163 | 2 |
| #3101 | 163 |