Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22627655 | C2 | semidirect |
| 2. C2×#22627650 | C2 | semidirect |
| 3. C2×#22627646 | C2 | semidirect |
| 4. #34036703 | C2 | semidirect |
| 5. #34036696 | C2 | semidirect |
| 6. #34036520 | C2 | semidirect |
| 7. #34036515 | C2 | semidirect |
| 8. #34036510 | C2 | semidirect |
| 9. #34036500 | C2 | semidirect |
| 10. #34036084 | C2 | semidirect |
| 11. C22×SD16×C293 | C2 | semidirect |
| 17. C2×Dic1172 | C22 | semidirect |
| 18. C2×#17989792 | C22 | semidirect |
| 19. C2×#17989791 | C22 | semidirect |
| 20. C2×#17989791 | C22 | semidirect |
| 22. C2×#17989789 | C22 | semidirect |
| 23. C2×D2344 | C22 | semidirect |
| 26. #22627622 | C22 | semidirect |
| 28. #22627613 | C22 | semidirect |
| 35. #22627534 | C22 | semidirect |
| 36. C8×Dic293 | C22 | semidirect |
| 64. #17989786 | D4 | semidirect |
| 85. C2×C8×C293 | D4 | semidirect |
| 148. C293 | #3154 | semidirect |
| 153. C22×SD16 | D293 | semidirect |
| 228. C2×C8 | C22⋊D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627655 | 2 |
| C2×#22627650 | 2 |
| C2×#22627646 | 2 |
| #34036703 | 2 |
| #34036696 | 2 |
| #34036520 | 2 |
| #34036515 | 2 |
| #34036510 | 2 |
| #34036500 | 2 |
| #34036084 | 2 |
| C22×SD16×C293 | 2 |
| #3154 | 293 |