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 |
|---|---|---|
| 1. #34036757 | C2 | semidirect |
| 3. #34036430 | C2 | semidirect |
| 4. #34036430 | C2 | semidirect |
| 5. #34036420 | C2 | semidirect |
| 6. #34036410 | C2 | semidirect |
| 7. #34036171 | C2 | semidirect |
| 8. #34036167 | C2 | semidirect |
| 11. #424×C293 | C2 | semidirect |
| 13. #22627624 | C22 | semidirect |
| 15. #22627616 | C22 | semidirect |
| 26. #22627558 | C22 | semidirect |
| 27. #22627558 | C22 | semidirect |
| 28. #22627558 | C22 | semidirect |
| 29. #22627556 | C22 | semidirect |
| 30. #22627556 | C22 | semidirect |
| 31. #22627556 | C22 | semidirect |
| 39. C4⋊C8×C293 | C22 | semidirect |
| 40. C4⋊C8×C293 | C22 | semidirect |
| 45. C2×D1172 | Q8 | semidirect |
| 124. C293 | #3081 | semidirect |
| 134. #424 | D293 | semidirect |
| 160. C4⋊C8 | C2×D293 | semidirect |
| 161. C4⋊C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036757 | 2 |
| #34036603 | 2 |
| #34036430 | 2 |
| #34036420 | 2 |
| #34036410 | 2 |
| #34036171 | 2 |
| #34036167 | 2 |
| #34036135 | 2 |
| C2×#22627546 | 2 |
| #424×C293 | 2 |
| #3081 | 293 |