Finite Group DatabasebetaFinite Group DatabasebetaOrder 18752.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22627670 | C2 | semidirect |
| 2. #22627655 | C2 | semidirect |
| 3. #22627649 | C2 | semidirect |
| 4. #22627644 | C2 | semidirect |
| 5. C2×#17989789 | C2 | semidirect |
| 6. #22627631 | C2 | semidirect |
| 7. 2−1+4×C293 | C2 | semidirect |
| 12. #17989792 | C22 | semidirect |
| 13. #17989790 | C22 | semidirect |
| 14. #17989789 | C22 | semidirect |
| 15. #17989789 | C22 | semidirect |
| 16. #17989787 | C22 | semidirect |
| 17. #17989786 | C22 | semidirect |
| 18. C2×#14556873 | C22 | semidirect |
| 21. #41×C293 | C22 | semidirect |
| 23. C2×Q8×C293 | C22 | semidirect |
| 53. C293 | #577 | semidirect |
| 55. 2−1+4 | D293 | semidirect |
| 66. #41 | C2×D293 | semidirect |
| 68. C2×Q8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627670 | 2 |
| #22627655 | 2 |
| #22627649 | 2 |
| #22627644 | 2 |
| C2×#17989789 | 2 |
| #22627631 | 2 |
| 2−1+4×C293 | 2 |
| #577 | 293 |