Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #34036925 | C2 | semidirect |
| 2. C2×#22627643 | C2 | semidirect |
| 3. #131×D293 | C2 | semidirect |
| 4. #34036405 | C2 | semidirect |
| 5. #34036404 | C2 | semidirect |
| 6. #34036396 | C2 | semidirect |
| 7. #34036391 | C2 | semidirect |
| 8. #34036390 | C2 | semidirect |
| 9. #108×D293 | C2 | semidirect |
| 10. #34036110 | C2 | semidirect |
| 11. #472×C293 | C2 | semidirect |
| 25. C2×Dic1172 | C22 | semidirect |
| 26. C2×#17989790 | C22 | semidirect |
| 37. #22627560 | C22 | semidirect |
| 38. #22627559 | C22 | semidirect |
| 39. #22627542 | C22 | semidirect |
| 40. #22627542 | C22 | semidirect |
| 41. #22627541 | C22 | semidirect |
| 43. C2×D8×C293 | C22 | semidirect |
| 45. #108×C293 | C22 | semidirect |
| 46. #100×C293 | C22 | semidirect |
| 166. C293 | #3067 | semidirect |
| 174. #472 | D293 | semidirect |
| 195. C2×D8 | C2×D293 | semidirect |
| 209. #108 | C2×D293 | semidirect |
| 213. #100 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036925 | 2 |
| C2×#22627643 | 2 |
| #131×D293 | 2 |
| #34036405 | 2 |
| #34036404 | 2 |
| #34036396 | 2 |
| #34036391 | 2 |
| #34036390 | 2 |
| #108×D293 | 2 |
| #34036110 | 2 |
| #472×C293 | 2 |
| #3067 | 293 |