Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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×#22627650 | C2 | semidirect |
| 2. #34036679 | C2 | semidirect |
| 3. #34036516 | C2 | semidirect |
| 4. #34036505 | C2 | semidirect |
| 5. #34036501 | C2 | semidirect |
| 6. C4×#17989786 | C2 | semidirect |
| 7. C2×#127×C293 | C2 | semidirect |
| 10. C2×#17989790 | C22 | semidirect |
| 11. C2×#17989787 | C22 | semidirect |
| 13. #22627624 | C22 | semidirect |
| 14. #22627621 | C22 | semidirect |
| 15. #22627612 | C22 | semidirect |
| 18. #22627535 | C22 | semidirect |
| 19. C4×#14556873 | C22 | semidirect |
| 34. #17989786 | D4 | semidirect |
| 57. #14556873 | C2×D4 | semidirect |
| 82. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 90. C293 | #3151 | semidirect |
| 94. C2×#127 | D293 | semidirect |
| 174. C4 | #22627650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627650 | 2 |
| #34036679 | 2 |
| #34036516 | 2 |
| #34036505 | 2 |
| #34036501 | 2 |
| C4×#17989786 | 2 |
| C2×#127×C293 | 2 |
| #3151 | 293 |