Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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. #34036477 | C2 | semidirect |
| 3. #34036453 | C2 | semidirect |
| 4. #34036411 | C2 | semidirect |
| 5. #34036360 | C2 | semidirect |
| 6. #34036329 | C2 | semidirect |
| 7. #34036289 | C2 | semidirect |
| 8. C4×#17989792 | C2 | semidirect |
| 9. D4×#14556873 | C2 | semidirect |
| 10. #34036123 | C2 | semidirect |
| 11. #556×C293 | C2 | semidirect |
| 127. C293 | #3304 | semidirect |
| 129. #556 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036800 | 2 |
| #34036477 | 2 |
| #34036453 | 2 |
| #34036411 | 2 |
| #34036360 | 2 |
| #34036329 | 2 |
| #34036289 | 2 |
| C4×#17989792 | 2 |
| D4×#14556873 | 2 |
| #34036123 | 2 |
| #556×C293 | 2 |
| #3304 | 293 |