Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26045787 | C2 | semidirect |
| 2. #26045783 | C2 | semidirect |
| 3. #26045782 | C2 | semidirect |
| 5. #26045772 | C2 | semidirect |
| 6. #26045771 | C2 | semidirect |
| 7. #26045757 | C2 | semidirect |
| 9. #26045751 | C2 | semidirect |
| 10. #26045750 | C2 | semidirect |
| 11. C2×C4⋊C4×C373 | C2 | semidirect |
| 72. C373 | #552 | semidirect |
| 84. C2×C4⋊C4 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045787 | 2 |
| #26045783 | 2 |
| #26045782 | 2 |
| #26045775 | 2 |
| #26045772 | 2 |
| #26045771 | 2 |
| #26045757 | 2 |
| C4×C22⋊D373 | 2 |
| #26045751 | 2 |
| #26045750 | 2 |
| C2×C4⋊C4×C373 | 2 |
| #552 | 373 |