Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 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. C2×#22627651 | C2 | semidirect |
| 2. #34036680 | C2 | semidirect |
| 3. C4×D4×D293 | C2 | semidirect |
| 4. #34036347 | C2 | semidirect |
| 5. #34036346 | C2 | semidirect |
| 6. #34036331 | C2 | semidirect |
| 7. #34036325 | C2 | semidirect |
| 8. #34036324 | C2 | semidirect |
| 9. #34036151 | C2 | semidirect |
| 10. #34036129 | C2 | semidirect |
| 11. #461×C293 | C2 | semidirect |
| 20. #22627621 | C22 | semidirect |
| 21. #22627613 | C22 | semidirect |
| 34. C4⋊#14556873 | C22 | semidirect |
| 35. #22627553 | C22 | semidirect |
| 36. #22627548 | C22 | semidirect |
| 37. #22627546 | C22 | semidirect |
| 38. #22627544 | C22 | semidirect |
| 40. C4⋊Q8×C293 | C22 | semidirect |
| 42. C4⋊C8×C293 | C22 | semidirect |
| 43. #103×C293 | C22 | semidirect |
| 54. D4×D293 | D4 | semidirect |
| 146. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 160. C293 | #3036 | semidirect |
| 168. #461 | D293 | semidirect |
| 182. C4⋊Q8 | C2×D293 | semidirect |
| 200. C4⋊C8 | C2×D293 | semidirect |
| 202. #103 | C2×D293 | semidirect |
| 311. C4 | #22627651 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627651 | 2 |
| #34036680 | 2 |
| C4×D4×D293 | 2 |
| #34036347 | 2 |
| #34036346 | 2 |
| #34036331 | 2 |
| #34036325 | 2 |
| #34036324 | 2 |
| #34036151 | 2 |
| #34036129 | 2 |
| #461×C293 | 2 |
| #3036 | 293 |