Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #34036757 | C2 | semidirect |
| 3. #34036432 | C2 | semidirect |
| 4. #34036428 | C2 | semidirect |
| 5. #34036418 | C2 | semidirect |
| 6. #34036408 | C2 | semidirect |
| 7. #34036172 | C2 | semidirect |
| 8. #34036155 | C2 | semidirect |
| 11. #427×C293 | C2 | semidirect |
| 15. #22627623 | C22 | semidirect |
| 17. #22627615 | C22 | semidirect |
| 26. #22627557 | C22 | semidirect |
| 27. #22627555 | C22 | semidirect |
| 28. #22627553 | C22 | semidirect |
| 29. #22627553 | C22 | semidirect |
| 37. #107×C293 | C22 | semidirect |
| 38. #107×C293 | C22 | semidirect |
| 39. #106×C293 | C22 | semidirect |
| 40. #106×C293 | C22 | semidirect |
| 45. C2×D1172 | Q8 | semidirect |
| 124. C293 | #3081 | semidirect |
| 133. #427 | D293 | semidirect |
| 155. #107 | C2×D293 | semidirect |
| 156. #107 | C2×D293 | semidirect |
| 158. #106 | C2×D293 | semidirect |
| 159. #106 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036757 | 2 |
| #34036603 | 2 |
| #34036432 | 2 |
| #34036428 | 2 |
| #34036418 | 2 |
| #34036408 | 2 |
| #34036172 | 2 |
| #34036155 | 2 |
| #34036133 | 2 |
| C2×#22627546 | 2 |
| #427×C293 | 2 |
| #3081 | 293 |