Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D293 |
| commutator, socle, cosocle | C22×C293 | C24 |
| Fitting | #120×C293 | C2 |
| hypercenter | #120 | D293 |
| hypocenter | C293 | #538 |
| LCS | G ▷ C22×C293 ▷ C293 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627617 | C2 | semidirect |
| 2. #22627617 | C2 | semidirect |
| 3. #22627611 | C2 | semidirect |
| 4. #22627610 | C2 | semidirect |
| 5. #22627606 | C2 | semidirect |
| 6. #22627605 | C2 | semidirect |
| 7. #22627601 | C2 | semidirect |
| 8. #22627596 | C2 | semidirect |
| 9. #22627596 | C2 | semidirect |
| 10. #22627595 | C2 | semidirect |
| 11. #22627593 | C2 | semidirect |
| 12. D4×Dic293 | C2 | semidirect |
| 13. #22627584 | C2 | semidirect |
| 14. C2×C22⋊Dic293 | C2 | semidirect |
| 15. #120×C293 | C2 | semidirect |
| 16. C2×Dic586 | C22 | semidirect |
| 20. C2×C22⋊D293 | C22 | semidirect |
| 23. C22×Dic293 | C22 | semidirect |
| 24. C2×C4×D293 | C22 | semidirect |
| 25. C4⋊Dic293 | C22 | semidirect |
| 26. C4⋊Dic293 | C22 | semidirect |
| 27. #17989781 | C22 | semidirect |
| 28. #17989781 | C22 | semidirect |
| 29. #17989781 | C22 | semidirect |
| 30. #17989781 | C22 | semidirect |
| 38. C22⋊Dic293 | C22 | semidirect |
| 39. C22⋊Dic293 | C22 | semidirect |
| 40. #17989779 | C22 | semidirect |
| 41. #17989779 | C22 | semidirect |
| 42. C4×Dic293 | C22 | semidirect |
| 43. C4×Dic293 | C22 | semidirect |
| 116. C293 | #538 | semidirect |
| 129. #120 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627617 | 2 |
| #22627611 | 2 |
| #22627610 | 2 |
| #22627606 | 2 |
| #22627605 | 2 |
| #22627601 | 2 |
| #22627596 | 2 |
| #22627595 | 2 |
| #22627593 | 2 |
| D4×Dic293 | 2 |
| #22627584 | 2 |
| C2×C22⋊Dic293 | 2 |
| #120×C293 | 2 |
| #538 | 293 |