Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #34036495 | C2 | semidirect |
| 3. #34036491 | C2 | semidirect |
| 4. #34036486 | C2 | semidirect |
| 5. #34036477 | C2 | semidirect |
| 6. #34036133 | C2 | semidirect |
| 7. #34036128 | C2 | semidirect |
| 8. #34036123 | C2 | semidirect |
| 9. C2×#22627544 | C2 | semidirect |
| 10. #34036085 | C2 | semidirect |
| 11. #544×C293 | C2 | semidirect |
| 21. #22627547 | C22 | semidirect |
| 22. #22627547 | C22 | semidirect |
| 23. #22627547 | C22 | semidirect |
| 28. #22627544 | C22 | semidirect |
| 29. #22627544 | C22 | semidirect |
| 30. #22627544 | C22 | semidirect |
| 31. #22627535 | C22 | semidirect |
| 32. C4×#14556873 | C22 | semidirect |
| 34. C4⋊Q8×C293 | C22 | semidirect |
| 36. #125×C293 | C22 | semidirect |
| 135. C293 | #3136 | semidirect |
| 137. #544 | D293 | semidirect |
| 153. C4⋊Q8 | C2×D293 | semidirect |
| 156. #125 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036698 | 2 |
| #34036495 | 2 |
| #34036491 | 2 |
| #34036486 | 2 |
| #34036477 | 2 |
| #34036133 | 2 |
| #34036128 | 2 |
| #34036123 | 2 |
| C2×#22627544 | 2 |
| #34036085 | 2 |
| #544×C293 | 2 |
| #3136 | 293 |