Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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. #34036896 | C2 | semidirect |
| 3. #34036133 | C2 | semidirect |
| 4. C2×#22627540 | C2 | semidirect |
| 5. #34035899 | C2 | semidirect |
| 6. #34035887 | C2 | semidirect |
| 7. #421×C293 | C2 | semidirect |
| 11. C2×#17989789 | C4 | semidirect |
| 12. C2×#17989787 | C4 | semidirect |
| 112. C293 | #1903 | semidirect |
| 116. #421 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627649 | 2 |
| #34036896 | 2 |
| #34036133 | 2 |
| C2×#22627540 | 2 |
| #34035899 | 2 |
| #34035887 | 2 |
| #421×C293 | 2 |
| #1903 | 293 |