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. #34036679 | C2 | semidirect |
| 2. C2×C4×D1172 | C2 | semidirect |
| 3. #34036448 | C2 | semidirect |
| 4. #34036420 | C2 | semidirect |
| 5. #34036325 | C2 | semidirect |
| 6. #34036265 | C2 | semidirect |
| 7. #34036242 | C2 | semidirect |
| 8. #432×C293 | C2 | semidirect |
| 13. #22627624 | C22 | semidirect |
| 14. #22627621 | C22 | semidirect |
| 23. C4×D1172 | C22 | semidirect |
| 26. #22627556 | C22 | semidirect |
| 28. #22627546 | C22 | semidirect |
| 30. C4⋊C8×C293 | C22 | semidirect |
| 32. #97×C293 | C22 | semidirect |
| 76. D1172 | #41 | semidirect |
| 120. C293 | #3109 | semidirect |
| 129. #432 | D293 | semidirect |
| 149. C4⋊C8 | C2×D293 | semidirect |
| 153. #97 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036679 | 2 |
| C2×C4×D1172 | 2 |
| #34036448 | 2 |
| #34036420 | 2 |
| #34036325 | 2 |
| #34036265 | 2 |
| #34036242 | 2 |
| #432×C293 | 2 |
| #3109 | 293 |