Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22627622 | C2 | semidirect |
| 2. #22627619 | C2 | semidirect |
| 3. #22627617 | C2 | semidirect |
| 4. #22627613 | C2 | semidirect |
| 5. #22627610 | C2 | semidirect |
| 6. #22627610 | C2 | semidirect |
| 7. #22627609 | C2 | semidirect |
| 8. #22627607 | C2 | semidirect |
| 9. #22627602 | C2 | semidirect |
| 10. #22627602 | C2 | semidirect |
| 12. #22627589 | C2 | semidirect |
| 13. C4×C22⋊D293 | C2 | semidirect |
| 14. #22627582 | C2 | semidirect |
| 15. C22⋊Q8×C293 | C2 | semidirect |
| 103. C293 | #542 | semidirect |
| 115. C22⋊Q8 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627622 | 2 |
| #22627619 | 2 |
| #22627617 | 2 |
| #22627613 | 2 |
| #22627610 | 2 |
| #22627609 | 2 |
| #22627607 | 2 |
| #22627602 | 2 |
| #22627597 | 2 |
| #22627589 | 2 |
| C4×C22⋊D293 | 2 |
| #22627582 | 2 |
| C22⋊Q8×C293 | 2 |
| #542 | 293 |