Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×D1172 | C2 | semidirect |
| 2. #34036445 | C2 | semidirect |
| 3. #34036416 | C2 | semidirect |
| 4. #34036321 | C2 | semidirect |
| 5. #34036262 | C2 | semidirect |
| 6. #34036239 | C2 | semidirect |
| 7. #34036186 | C2 | semidirect |
| 8. #532×C293 | C2 | semidirect |
| 18. #22627555 | C22 | semidirect |
| 19. C4⋊#14556873 | C22 | semidirect |
| 20. #22627545 | C22 | semidirect |
| 23. #22627535 | C22 | semidirect |
| 25. C4⋊Q8×C293 | C22 | semidirect |
| 26. #127×C293 | C22 | semidirect |
| 31. C4×D4×C293 | C22 | semidirect |
| 71. D1172 | #41 | semidirect |
| 120. C293 | #3109 | semidirect |
| 122. #532 | D293 | semidirect |
| 134. C4⋊Q8 | C2×D293 | semidirect |
| 135. #127 | C2×D293 | semidirect |
| 144. C4×D4 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1172 | 2 |
| #34036445 | 2 |
| #34036416 | 2 |
| #34036321 | 2 |
| #34036262 | 2 |
| #34036239 | 2 |
| #34036186 | 2 |
| #532×C293 | 2 |
| #3109 | 293 |