Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
778 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 253 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×#22627631 | C2 | semidirect |
| 3. #34036133 | C2 | semidirect |
| 4. #34036128 | C2 | semidirect |
| 5. #34036123 | C2 | semidirect |
| 6. C2×#22627544 | C2 | semidirect |
| 7. #520×C293 | C2 | semidirect |
| 9. #22627670 | C4 | semidirect |
| 15. C2×#17989786 | C22 | semidirect |
| 16. C22×#14556873 | C22 | semidirect |
| 17. #22627547 | C22 | semidirect |
| 18. #22627547 | C22 | semidirect |
| 19. #22627544 | C22 | semidirect |
| 20. #22627544 | C22 | semidirect |
| 21. #22627544 | C22 | semidirect |
| 25. #117×C293 | C22 | semidirect |
| 26. C2×C4⋊C4×C293 | C22 | semidirect |
| 30. #17989802 | C2×C4 | semidirect |
| 34. C2×D1172 | C2×C4 | semidirect |
| 97. C293 | #2897 | semidirect |
| 101. #520 | D293 | semidirect |
| 118. #117 | C2×D293 | semidirect |
| 119. C2×C4⋊C4 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627670 | 2 |
| C2×#22627631 | 2 |
| #34036133 | 2 |
| #34036128 | 2 |
| #34036123 | 2 |
| C2×#22627544 | 2 |
| #520×C293 | 2 |
| #2897 | 293 |