Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #22627632 | C2 | semidirect |
| 3. #22627631 | C2 | semidirect |
| 4. #22627559 | C2 | semidirect |
| 5. #22627552 | C2 | semidirect |
| 6. #22627535 | C2 | semidirect |
| 7. #104×C293 | C2 | semidirect |
| 9. #17989792 | C4 | semidirect |
| 10. #17989790 | C4 | semidirect |
| 11. #17989789 | C4 | semidirect |
| 12. #17989787 | C4 | semidirect |
| 51. C293 | #444 | semidirect |
| 58. #104 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627644 | 2 |
| #22627632 | 2 |
| #22627631 | 2 |
| #22627559 | 2 |
| #22627552 | 2 |
| #22627535 | 2 |
| #104×C293 | 2 |
| #444 | 293 |