Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #34036426 | C2 | semidirect |
| 3. #34036426 | C2 | semidirect |
| 4. #34036416 | C2 | semidirect |
| 5. #34036406 | C2 | semidirect |
| 6. #34036169 | C2 | semidirect |
| 7. #34036165 | C2 | semidirect |
| 8. #34036156 | C2 | semidirect |
| 11. #544×C293 | C2 | semidirect |
| 21. #22627557 | C22 | semidirect |
| 22. #22627557 | C22 | semidirect |
| 23. #22627557 | C22 | semidirect |
| 24. #22627555 | C22 | semidirect |
| 25. #22627555 | C22 | semidirect |
| 26. #22627555 | C22 | semidirect |
| 27. C4⋊#14556873 | C22 | semidirect |
| 28. C4⋊#14556873 | C22 | semidirect |
| 34. C4⋊Q8×C293 | C22 | semidirect |
| 36. #125×C293 | C22 | semidirect |
| 44. C2×D1172 | Q8 | semidirect |
| 124. C293 | #3081 | semidirect |
| 126. #544 | D293 | semidirect |
| 141. C4⋊Q8 | C2×D293 | semidirect |
| 143. #125 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036603 | 2 |
| #34036426 | 2 |
| #34036416 | 2 |
| #34036406 | 2 |
| #34036169 | 2 |
| #34036165 | 2 |
| #34036156 | 2 |
| #34036133 | 2 |
| C2×#22627544 | 2 |
| #544×C293 | 2 |
| #3081 | 293 |