Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #34036684 | C2 | semidirect |
| 3. #34036428 | C2 | semidirect |
| 4. #34036427 | C2 | semidirect |
| 5. #34036416 | C2 | semidirect |
| 6. #34036410 | C2 | semidirect |
| 7. #34036409 | C2 | semidirect |
| 8. #34036168 | C2 | semidirect |
| 9. #34036151 | C2 | semidirect |
| 11. #476×C293 | C2 | semidirect |
| 15. #22627624 | C22 | semidirect |
| 16. #22627615 | C22 | semidirect |
| 30. #22627558 | C22 | semidirect |
| 31. #22627557 | C22 | semidirect |
| 32. #22627555 | C22 | semidirect |
| 33. C4⋊#14556873 | C22 | semidirect |
| 34. #22627553 | C22 | semidirect |
| 38. C4⋊Q8×C293 | C22 | semidirect |
| 40. #106×C293 | C22 | semidirect |
| 41. C4⋊C8×C293 | C22 | semidirect |
| 48. D4×D293 | Q8 | semidirect |
| 144. C293 | #3077 | semidirect |
| 151. #476 | D293 | semidirect |
| 161. C4⋊Q8 | C2×D293 | semidirect |
| 180. #106 | C2×D293 | semidirect |
| 183. C4⋊C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036684 | 2 |
| C4×D4×D293 | 2 |
| #34036428 | 2 |
| #34036427 | 2 |
| #34036416 | 2 |
| #34036410 | 2 |
| #34036409 | 2 |
| #34036168 | 2 |
| #34036151 | 2 |
| #34036132 | 2 |
| #476×C293 | 2 |
| #3077 | 293 |