Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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×#22627657 | C2 | semidirect |
| 3. C22×#17989792 | C2 | semidirect |
| 4. #34036703 | C2 | semidirect |
| 5. #34036700 | C2 | semidirect |
| 6. #34036522 | C2 | semidirect |
| 7. #34036520 | C2 | semidirect |
| 8. #34036510 | C2 | semidirect |
| 9. #34036507 | C2 | semidirect |
| 10. #34036087 | C2 | semidirect |
| 11. C2×#137×C293 | C2 | semidirect |
| 143. C293 | #3156 | semidirect |
| 146. C2×#137 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627657 | 2 |
| C2×#22627644 | 2 |
| C22×#17989792 | 2 |
| #34036703 | 2 |
| #34036700 | 2 |
| #34036522 | 2 |
| #34036520 | 2 |
| #34036510 | 2 |
| #34036507 | 2 |
| #34036087 | 2 |
| C2×#137×C293 | 2 |
| #3156 | 293 |