Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
462 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 139 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. #34036836 | C2 | semidirect |
| 3. #34036476 | C2 | semidirect |
| 4. #34036448 | C2 | semidirect |
| 5. #34036420 | C2 | semidirect |
| 6. #34036358 | C2 | semidirect |
| 7. #34036330 | C2 | semidirect |
| 8. #34036282 | C2 | semidirect |
| 9. C4×#17989791 | C2 | semidirect |
| 10. C2×#22627546 | C2 | semidirect |
| 11. C8×D4×C293 | C2 | semidirect |
| 15. C2×#17989791 | C22 | semidirect |
| 16. #22627624 | C22 | semidirect |
| 19. #22627603 | C22 | semidirect |
| 24. C4×Dic586 | C22 | semidirect |
| 27. C2×C4⋊Dic293 | C22 | semidirect |
| 28. #22627556 | C22 | semidirect |
| 29. #22627556 | C22 | semidirect |
| 30. #22627549 | C22 | semidirect |
| 33. #22627546 | C22 | semidirect |
| 34. #22627546 | C22 | semidirect |
| 35. #22627546 | C22 | semidirect |
| 36. C22×C8×C293 | C22 | semidirect |
| 38. C4⋊C8×C293 | C22 | semidirect |
| 39. C22⋊C8×C293 | C22 | semidirect |
| 40. C4×C8×C293 | C22 | semidirect |
| 100. D4×C293 | SD16 | semidirect |
| 136. C293 | #3295 | semidirect |
| 147. C8×D4 | D293 | semidirect |
| 153. C22×C8 | C2×D293 | semidirect |
| 169. C4⋊C8 | C2×D293 | semidirect |
| 176. C22⋊C8 | C2×D293 | semidirect |
| 177. C4×C8 | C2×D293 | semidirect |
| 231. D4 | #17989791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036836 | 2 |
| D4×D1172 | 2 |
| #34036476 | 2 |
| #34036448 | 2 |
| #34036420 | 2 |
| #34036358 | 2 |
| #34036330 | 2 |
| #34036282 | 2 |
| C4×#17989791 | 2 |
| C2×#22627546 | 2 |
| C8×D4×C293 | 2 |
| #3295 | 293 |