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. #22627671 | C2 | semidirect |
| 2. #22627670 | C2 | semidirect |
| 3. #22627657 | C2 | semidirect |
| 4. #22627652 | C2 | semidirect |
| 5. #22627646 | C2 | semidirect |
| 6. C2×#17989791 | C2 | semidirect |
| 7. #131×C293 | C2 | semidirect |
| 10. #17989802 | C22 | semidirect |
| 12. C2×Dic586 | C22 | semidirect |
| 16. Dic1172 | C22 | semidirect |
| 17. #17989791 | C22 | semidirect |
| 18. #17989791 | C22 | semidirect |
| 19. #17989791 | C22 | semidirect |
| 20. D2344 | C22 | semidirect |
| 22. M16×C293 | C22 | semidirect |
| 23. C2×C8×C293 | C22 | semidirect |
| 53. C293 | #577 | semidirect |
| 61. #131 | D293 | semidirect |
| 76. M16 | C2×D293 | semidirect |
| 77. C2×C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627671 | 2 |
| #22627670 | 2 |
| #22627657 | 2 |
| #22627652 | 2 |
| #22627646 | 2 |
| C2×#17989791 | 2 |
| #131×C293 | 2 |
| #577 | 293 |