Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 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. #22627619 | C2 | semidirect |
| 2. #22627617 | C2 | semidirect |
| 3. #22627614 | C2 | semidirect |
| 4. #22627610 | C2 | semidirect |
| 5. #22627609 | C2 | semidirect |
| 6. #22627606 | C2 | semidirect |
| 7. #22627602 | C2 | semidirect |
| 9. C4×Dic586 | C2 | semidirect |
| 10. C4×D1172 | C2 | semidirect |
| 11. C4×C22⋊D293 | C2 | semidirect |
| 12. C4×C22⋊D293 | C2 | semidirect |
| 13. #22627581 | C2 | semidirect |
| 14. C42×D293 | C2 | semidirect |
| 15. #117×C293 | C2 | semidirect |
| 103. C293 | #529 | semidirect |
| 118. #117 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627619 | 2 |
| #22627617 | 2 |
| #22627614 | 2 |
| #22627610 | 2 |
| #22627609 | 2 |
| #22627606 | 2 |
| #22627602 | 2 |
| #22627597 | 2 |
| C4×Dic586 | 2 |
| C4×D1172 | 2 |
| C4×C22⋊D293 | 2 |
| #22627581 | 2 |
| C42×D293 | 2 |
| #117×C293 | 2 |
| #529 | 293 |