Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
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. #22627617 | C2 | semidirect |
| 2. #22627617 | C2 | semidirect |
| 3. #22627610 | C2 | semidirect |
| 4. #22627608 | C2 | semidirect |
| 5. #22627607 | C2 | semidirect |
| 6. #22627606 | C2 | semidirect |
| 7. #22627603 | C2 | semidirect |
| 8. #22627601 | C2 | semidirect |
| 10. C4×C22⋊D293 | C2 | semidirect |
| 11. #22627584 | C2 | semidirect |
| 12. #22627583 | C2 | semidirect |
| 13. #22627580 | C2 | semidirect |
| 14. C2×C22⋊Dic293 | C2 | semidirect |
| 15. C2×C22⋊C4×C293 | C2 | semidirect |
| 16. C2×Dic586 | C22 | semidirect |
| 22. C2×C4×D293 | C22 | semidirect |
| 23. C4⋊Dic293 | C22 | semidirect |
| 24. C4⋊Dic293 | C22 | semidirect |
| 25. C4⋊Dic293 | C22 | semidirect |
| 26. #17989781 | C22 | semidirect |
| 27. #17989781 | C22 | semidirect |
| 28. #17989781 | C22 | semidirect |
| 29. #17989781 | C22 | semidirect |
| 30. #17989781 | C22 | semidirect |
| 38. #17989779 | C22 | semidirect |
| 39. #17989779 | C22 | semidirect |
| 40. #17989779 | C22 | semidirect |
| 41. C4×Dic293 | C22 | semidirect |
| 42. C4×Dic293 | C22 | semidirect |
| 43. C4×Dic293 | C22 | semidirect |
| 110. C293 | #551 | semidirect |
| 126. C2×C22⋊C4 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627617 | 2 |
| #22627610 | 2 |
| #22627608 | 2 |
| #22627607 | 2 |
| #22627606 | 2 |
| #22627603 | 2 |
| #22627601 | 2 |
| #22627593 | 2 |
| C4×C22⋊D293 | 2 |
| #22627584 | 2 |
| #22627583 | 2 |
| #22627580 | 2 |
| C2×C22⋊Dic293 | 2 |
| C2×C22⋊C4×C293 | 2 |
| #551 | 293 |