Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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. #127×D293 | C2 | semidirect |
| 4. #34036515 | C2 | semidirect |
| 5. #34036506 | C2 | semidirect |
| 6. #34036505 | C2 | semidirect |
| 7. #34036503 | C2 | semidirect |
| 8. C4×#17989785 | C2 | semidirect |
| 9. #492×C293 | C2 | semidirect |
| 14. C2×#17989789 | C22 | semidirect |
| 15. C2×D2344 | C22 | semidirect |
| 16. C2×#17989787 | C22 | semidirect |
| 19. #22627621 | C22 | semidirect |
| 22. #22627613 | C22 | semidirect |
| 26. #22627534 | C22 | semidirect |
| 27. C4×#14556873 | C22 | semidirect |
| 28. C2×SD16×C293 | C22 | semidirect |
| 29. C4⋊Q8×C293 | C22 | semidirect |
| 31. C4×C8×C293 | C22 | semidirect |
| 49. #17989785 | D4 | semidirect |
| 78. #14556873 | C2×D4 | semidirect |
| 86. C8×C293 | C2×D4 | semidirect |
| 98. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 108. C293 | #3151 | semidirect |
| 117. #492 | D293 | semidirect |
| 124. C2×SD16 | C2×D293 | semidirect |
| 128. C4⋊Q8 | C2×D293 | semidirect |
| 140. C4×C8 | C2×D293 | semidirect |
| 195. C8 | D4×D293 | semidirect |
| 209. 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 |
| #127×D293 | 2 |
| #34036515 | 2 |
| #34036506 | 2 |
| #34036505 | 2 |
| #34036503 | 2 |
| C4×#17989785 | 2 |
| #492×C293 | 2 |
| #3151 | 293 |