Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22627652 | C2 | semidirect |
| 2. #34036679 | C2 | semidirect |
| 3. C2×C4×D1172 | C2 | semidirect |
| 4. #34036345 | C2 | semidirect |
| 5. #34036335 | C2 | semidirect |
| 6. #34036325 | C2 | semidirect |
| 7. #34036131 | C2 | semidirect |
| 8. #423×C293 | C2 | semidirect |
| 15. #22627624 | C22 | semidirect |
| 16. #22627621 | C22 | semidirect |
| 17. #22627612 | C22 | semidirect |
| 28. #22627549 | C22 | semidirect |
| 29. #22627546 | C22 | semidirect |
| 32. C4⋊C8×C293 | C22 | semidirect |
| 33. C4⋊C8×C293 | C22 | semidirect |
| 42. C2×D1172 | D4 | semidirect |
| 118. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 129. C293 | #3036 | semidirect |
| 137. #423 | D293 | semidirect |
| 160. C4⋊C8 | C2×D293 | semidirect |
| 161. C4⋊C8 | C2×D293 | semidirect |
| 250. C4 | #22627652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627652 | 2 |
| #34036679 | 2 |
| C2×C4×D1172 | 2 |
| #34036345 | 2 |
| #34036335 | 2 |
| #34036325 | 2 |
| #34036131 | 2 |
| #423×C293 | 2 |
| #3036 | 293 |