Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#22627559 | C2 | semidirect |
| 5. #34035888 | C2 | semidirect |
| 6. #34035883 | C2 | semidirect |
| 7. #424×C293 | C2 | semidirect |
| 18. #22627547 | C4 | semidirect |
| 19. #22627547 | C4 | semidirect |
| 20. #22627544 | C4 | semidirect |
| 21. #22627544 | C4 | semidirect |
| 109. C293 | #1866 | semidirect |
| 113. #424 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627630 | 2 |
| C2×#22627559 | 2 |
| C2×#22627550 | 2 |
| #34036123 | 2 |
| #34035888 | 2 |
| #34035883 | 2 |
| #424×C293 | 2 |
| #1866 | 293 |