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×#22627654 | C2 | semidirect |
| 2. C2×#22627650 | C2 | semidirect |
| 3. C2×#22627644 | C2 | semidirect |
| 4. C22×#17989790 | C2 | semidirect |
| 5. #34036705 | C2 | semidirect |
| 6. #34036524 | C2 | semidirect |
| 7. #34036516 | C2 | semidirect |
| 8. #34036511 | C2 | semidirect |
| 9. #34036501 | C2 | semidirect |
| 10. #34036085 | C2 | semidirect |
| 11. #535×C293 | C2 | semidirect |
| 17. C2×#17989792 | C22 | semidirect |
| 18. C2×#17989792 | C22 | semidirect |
| 23. C2×#17989790 | C22 | semidirect |
| 24. C2×#17989790 | C22 | semidirect |
| 25. C2×#17989789 | C22 | semidirect |
| 27. C2×#17989787 | C22 | semidirect |
| 30. #22627624 | C22 | semidirect |
| 31. #22627612 | C22 | semidirect |
| 34. #22627535 | C22 | semidirect |
| 35. C4×#14556873 | C22 | semidirect |
| 64. #17989786 | D4 | semidirect |
| 65. C2×#14556873 | D4 | semidirect |
| 148. C293 | #3154 | semidirect |
| 155. #535 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627654 | 2 |
| C2×#22627650 | 2 |
| C2×#22627644 | 2 |
| C22×#17989790 | 2 |
| #34036705 | 2 |
| #34036524 | 2 |
| #34036516 | 2 |
| #34036511 | 2 |
| #34036501 | 2 |
| #34036085 | 2 |
| #535×C293 | 2 |
| #3154 | 293 |