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. #34036677 | C2 | semidirect |
| 2. C4×#17989801 | C2 | semidirect |
| 3. #34036452 | C2 | semidirect |
| 4. #34036415 | C2 | semidirect |
| 5. #34036409 | C2 | semidirect |
| 6. #34036326 | C2 | semidirect |
| 7. #34036271 | C2 | semidirect |
| 8. #34036241 | C2 | semidirect |
| 9. #34036226 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #459×C293 | C2 | semidirect |
| 86. Dic586 | #41 | semidirect |
| 110. D4×C293 | #41 | semidirect |
| 144. C293 | #3115 | semidirect |
| 152. #459 | D293 | semidirect |
| 241. D4 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036677 | 2 |
| C4×#17989801 | 2 |
| #34036452 | 2 |
| #34036415 | 2 |
| #34036409 | 2 |
| #34036326 | 2 |
| #34036271 | 2 |
| #34036241 | 2 |
| #34036226 | 2 |
| #34036185 | 2 |
| #459×C293 | 2 |
| #3115 | 293 |