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×#17989801 | C2 | semidirect |
| 3. #34036456 | C2 | semidirect |
| 4. #34036411 | C2 | semidirect |
| 5. #34036330 | C2 | semidirect |
| 6. #34036324 | C2 | semidirect |
| 7. #34036275 | C2 | semidirect |
| 8. #34036238 | C2 | semidirect |
| 9. #34036228 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #474×C293 | C2 | semidirect |
| 86. Dic586 | #41 | semidirect |
| 109. D4×C293 | #41 | semidirect |
| 144. C293 | #3115 | semidirect |
| 150. #474 | D293 | semidirect |
| 241. D4 | #17989803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036680 | 2 |
| C4×#17989801 | 2 |
| #34036456 | 2 |
| #34036411 | 2 |
| #34036330 | 2 |
| #34036324 | 2 |
| #34036275 | 2 |
| #34036238 | 2 |
| #34036228 | 2 |
| #34036185 | 2 |
| #474×C293 | 2 |
| #3115 | 293 |