Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22627632 | C2 | semidirect |
| 2. C22×#17989785 | C2 | semidirect |
| 4. #34036206 | C2 | semidirect |
| 5. #34036199 | C2 | semidirect |
| 6. #34036095 | C2 | semidirect |
| 7. #34036092 | C2 | semidirect |
| 8. #34036085 | C2 | semidirect |
| 9. #424×C293 | C2 | semidirect |
| 17. C2×#17989785 | C22 | semidirect |
| 19. C2×C8×D293 | C22 | semidirect |
| 26. #22627536 | C22 | semidirect |
| 27. #22627535 | C22 | semidirect |
| 28. C4×#14556873 | C22 | semidirect |
| 32. C4⋊C8×C293 | C22 | semidirect |
| 50. C2×#14556873 | D4 | semidirect |
| 113. C293 | #2930 | semidirect |
| 120. #424 | D293 | semidirect |
| 142. C4⋊C8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627632 | 2 |
| C22×#17989785 | 2 |
| #34036641 | 2 |
| #34036206 | 2 |
| #34036199 | 2 |
| #34036095 | 2 |
| #34036092 | 2 |
| #34036085 | 2 |
| #424×C293 | 2 |
| #2930 | 293 |