Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26045785 | C2 | semidirect |
| 3. #26045782 | C2 | semidirect |
| 4. #26045778 | C2 | semidirect |
| 5. #26045776 | C2 | semidirect |
| 6. #26045773 | C2 | semidirect |
| 7. #26045769 | C2 | semidirect |
| 9. C4×Dic746 | C2 | semidirect |
| 10. C4×C22⋊D373 | C2 | semidirect |
| 11. C4×C22⋊D373 | C2 | semidirect |
| 12. #26045751 | C2 | semidirect |
| 13. #26045749 | C2 | semidirect |
| 14. C2×C4×Dic373 | C2 | semidirect |
| 15. C4×D4×C373 | C2 | semidirect |
| 103. C373 | #529 | semidirect |
| 116. C4×D4 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045787 | 2 |
| #26045785 | 2 |
| #26045782 | 2 |
| #26045778 | 2 |
| #26045776 | 2 |
| #26045773 | 2 |
| #26045769 | 2 |
| #26045764 | 2 |
| C4×Dic746 | 2 |
| C4×C22⋊D373 | 2 |
| #26045751 | 2 |
| #26045749 | 2 |
| C2×C4×Dic373 | 2 |
| C4×D4×C373 | 2 |
| #529 | 373 |