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 |
|---|---|---|
| 1. #34036849 | C2 | semidirect |
| 3. #34036480 | C2 | semidirect |
| 4. #34036471 | C2 | semidirect |
| 5. #34036410 | C2 | semidirect |
| 6. #34036370 | C2 | semidirect |
| 7. #34036340 | C2 | semidirect |
| 8. #34036293 | C2 | semidirect |
| 9. C4×#17989791 | C2 | semidirect |
| 10. #34036126 | C2 | semidirect |
| 11. C8×D4×C293 | C2 | semidirect |
| 125. C293 | #3302 | semidirect |
| 136. C8×D4 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036849 | 2 |
| #34036784 | 2 |
| #34036480 | 2 |
| #34036471 | 2 |
| #34036410 | 2 |
| #34036370 | 2 |
| #34036340 | 2 |
| #34036293 | 2 |
| C4×#17989791 | 2 |
| #34036126 | 2 |
| C8×D4×C293 | 2 |
| #3302 | 293 |