Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #34036467 | C2 | semidirect |
| 3. #34036421 | C2 | semidirect |
| 4. #34036416 | C2 | semidirect |
| 5. #34036336 | C2 | semidirect |
| 6. #34036331 | C2 | semidirect |
| 8. #34036234 | C2 | semidirect |
| 9. #34036227 | C2 | semidirect |
| 10. #34036186 | C2 | semidirect |
| 11. #533×C293 | C2 | semidirect |
| 136. C293 | #3116 | semidirect |
| 138. #533 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17989802 | 2 |
| #34036467 | 2 |
| #34036421 | 2 |
| #34036416 | 2 |
| #34036336 | 2 |
| #34036331 | 2 |
| #34036289 | 2 |
| #34036234 | 2 |
| #34036227 | 2 |
| #34036186 | 2 |
| #533×C293 | 2 |
| #3116 | 293 |