Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26045791 | C2 | semidirect |
| 2. #26045790 | C2 | semidirect |
| 3. #26045787 | C2 | semidirect |
| 4. #26045787 | C2 | semidirect |
| 5. #26045785 | C2 | semidirect |
| 6. #26045785 | C2 | semidirect |
| 7. #26045783 | C2 | semidirect |
| 8. #26045782 | C2 | semidirect |
| 12. #26045771 | C2 | semidirect |
| 13. #26045770 | C2 | semidirect |
| 14. #26045768 | C2 | semidirect |
| 15. C22⋊Q8×C373 | C2 | semidirect |
| 97. C373 | #563 | semidirect |
| 113. C22⋊Q8 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045791 | 2 |
| #26045790 | 2 |
| #26045787 | 2 |
| #26045785 | 2 |
| #26045783 | 2 |
| #26045782 | 2 |
| #26045778 | 2 |
| #26045775 | 2 |
| #26045774 | 2 |
| #26045771 | 2 |
| #26045770 | 2 |
| #26045768 | 2 |
| C22⋊Q8×C373 | 2 |
| #563 | 373 |