Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 2. #23782031 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781669 | C2 | semidirect |
| 5. C4×#14579683 | C2 | semidirect |
| 6. #533×C163 | C2 | semidirect |
| 13. #19104655 | C22 | semidirect |
| 14. #19104646 | C22 | semidirect |
| 15. C4×C163⋊C8 | C22 | semidirect |
| 16. C4⋊Q8×C163 | C22 | semidirect |
| 17. #125×C163 | C22 | semidirect |
| 74. C163 | #3138 | semidirect |
| 76. #533 | D163 | semidirect |
| 85. C4⋊Q8 | C2×D163 | semidirect |
| 89. #125 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104732 | 2 |
| #23782031 | 2 |
| #23782013 | 2 |
| #23781669 | 2 |
| C4×#14579683 | 2 |
| #533×C163 | 2 |
| #3138 | 163 |