Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #34036481 | C2 | semidirect |
| 3. #34036470 | C2 | semidirect |
| 4. #34036406 | C2 | semidirect |
| 5. #34036368 | C2 | semidirect |
| 6. #34036339 | C2 | semidirect |
| 7. #34036289 | C2 | semidirect |
| 8. C4×#17989789 | C2 | semidirect |
| 9. D4×#14556873 | C2 | semidirect |
| 10. #34036123 | C2 | semidirect |
| 11. #556×C293 | C2 | semidirect |
| 125. C293 | #3302 | semidirect |
| 127. #556 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036784 | 2 |
| #34036481 | 2 |
| #34036470 | 2 |
| #34036406 | 2 |
| #34036368 | 2 |
| #34036339 | 2 |
| #34036289 | 2 |
| C4×#17989789 | 2 |
| D4×#14556873 | 2 |
| #34036123 | 2 |
| #556×C293 | 2 |
| #3302 | 293 |