Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #34036680 | C2 | semidirect |
| 2. C4×#17989803 | C2 | semidirect |
| 3. #34036455 | C2 | semidirect |
| 4. #34036406 | C2 | semidirect |
| 5. #34036329 | C2 | semidirect |
| 6. #34036325 | C2 | semidirect |
| 7. #34036277 | C2 | semidirect |
| 8. #34036240 | C2 | semidirect |
| 9. #34036232 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #475×C293 | C2 | semidirect |
| 93. D1172 | #41 | semidirect |
| 109. Q8×C293 | #41 | semidirect |
| 144. C293 | #3115 | semidirect |
| 149. #475 | D293 | semidirect |
| 233. Q8 | #17989803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036680 | 2 |
| C4×#17989803 | 2 |
| #34036455 | 2 |
| #34036406 | 2 |
| #34036329 | 2 |
| #34036325 | 2 |
| #34036277 | 2 |
| #34036240 | 2 |
| #34036232 | 2 |
| #34036185 | 2 |
| #475×C293 | 2 |
| #3115 | 293 |