Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #26045785 | C2 | semidirect |
| 2. #26045785 | C2 | semidirect |
| 3. #26045778 | C2 | semidirect |
| 4. #26045776 | C2 | semidirect |
| 5. #26045775 | C2 | semidirect |
| 6. #26045774 | C2 | semidirect |
| 7. #26045771 | C2 | semidirect |
| 8. #26045769 | C2 | semidirect |
| 10. C4×C22⋊D373 | C2 | semidirect |
| 11. #26045752 | C2 | semidirect |
| 12. #26045751 | C2 | semidirect |
| 13. #26045748 | C2 | semidirect |
| 14. C2×C22⋊Dic373 | C2 | semidirect |
| 15. C2×C22⋊C4×C373 | C2 | semidirect |
| 16. C2×Dic746 | C22 | semidirect |
| 22. C2×C4×D373 | C22 | semidirect |
| 23. C4⋊Dic373 | C22 | semidirect |
| 24. C4⋊Dic373 | C22 | semidirect |
| 25. C4⋊Dic373 | C22 | semidirect |
| 26. #20238589 | C22 | semidirect |
| 27. #20238589 | C22 | semidirect |
| 28. #20238589 | C22 | semidirect |
| 29. #20238589 | C22 | semidirect |
| 30. #20238589 | C22 | semidirect |
| 38. #20238587 | C22 | semidirect |
| 39. #20238587 | C22 | semidirect |
| 40. #20238587 | C22 | semidirect |
| 41. C4×Dic373 | C22 | semidirect |
| 42. C4×Dic373 | C22 | semidirect |
| 43. C4×Dic373 | C22 | semidirect |
| 110. C373 | #551 | semidirect |
| 126. C2×C22⋊C4 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045785 | 2 |
| #26045778 | 2 |
| #26045776 | 2 |
| #26045775 | 2 |
| #26045774 | 2 |
| #26045771 | 2 |
| #26045769 | 2 |
| #26045761 | 2 |
| C4×C22⋊D373 | 2 |
| #26045752 | 2 |
| #26045751 | 2 |
| #26045748 | 2 |
| C2×C22⋊Dic373 | 2 |
| C2×C22⋊C4×C373 | 2 |
| #551 | 373 |