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. #26045783 | C2 | semidirect |
| 5. #26045768 | C2 | semidirect |
| 6. Q8×Dic373 | C2 | semidirect |
| 8. #26045750 | C2 | semidirect |
| 9. #26045748 | C2 | semidirect |
| 10. C2×C4⋊Dic373 | C2 | semidirect |
| 11. C22⋊Q8×C373 | C2 | semidirect |
| 72. C373 | #552 | semidirect |
| 79. C22⋊Q8 | 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 |
| #26045776 | 2 |
| #26045768 | 2 |
| Q8×Dic373 | 2 |
| C4×C22⋊D373 | 2 |
| #26045750 | 2 |
| #26045748 | 2 |
| C2×C4⋊Dic373 | 2 |
| C22⋊Q8×C373 | 2 |
| #552 | 373 |