Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#22627649 | C2 | semidirect |
| 3. #34036675 | C2 | semidirect |
| 4. C2×#22627586 | C2 | semidirect |
| 5. #34036347 | C2 | semidirect |
| 6. #34036343 | C2 | semidirect |
| 7. #34036333 | C2 | semidirect |
| 8. #34036323 | C2 | semidirect |
| 9. #34036152 | C2 | semidirect |
| 10. #34036128 | C2 | semidirect |
| 11. #417×C293 | C2 | semidirect |
| 22. #22627622 | C22 | semidirect |
| 23. #22627620 | C22 | semidirect |
| 24. #22627613 | C22 | semidirect |
| 25. #22627611 | C22 | semidirect |
| 36. #22627553 | C22 | semidirect |
| 37. #22627553 | C22 | semidirect |
| 38. #22627547 | C22 | semidirect |
| 39. #22627544 | C22 | semidirect |
| 43. #103×C293 | C22 | semidirect |
| 44. #102×C293 | C22 | semidirect |
| 51. C2×D1172 | D4 | semidirect |
| 158. Dic293 | AGL(1,ℤ/8) | semidirect |
| 166. C293 | #3036 | semidirect |
| 178. #417 | D293 | semidirect |
| 209. #103 | C2×D293 | semidirect |
| 211. #102 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627652 | 2 |
| C2×#22627649 | 2 |
| #34036675 | 2 |
| C2×#22627586 | 2 |
| #34036347 | 2 |
| #34036343 | 2 |
| #34036333 | 2 |
| #34036323 | 2 |
| #34036152 | 2 |
| #34036128 | 2 |
| #417×C293 | 2 |
| #3036 | 293 |