Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22627657 | C2 | semidirect |
| 2. C2×#22627644 | C2 | semidirect |
| 3. C22×#17989790 | C2 | semidirect |
| 4. #34036700 | C2 | semidirect |
| 5. #34036696 | C2 | semidirect |
| 6. #34036520 | C2 | semidirect |
| 7. #34036517 | C2 | semidirect |
| 8. #34036512 | C2 | semidirect |
| 9. #34036500 | C2 | semidirect |
| 10. #34036087 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C293 | C2 | semidirect |
| 16. C2×Dic1172 | C22 | semidirect |
| 17. C2×#17989792 | C22 | semidirect |
| 18. C2×#17989791 | C22 | semidirect |
| 22. C2×#17989790 | C22 | semidirect |
| 23. C2×#17989789 | C22 | semidirect |
| 24. C2×#17989787 | C22 | semidirect |
| 26. #22627622 | C22 | semidirect |
| 29. #22627611 | C22 | semidirect |
| 35. #22627534 | C22 | semidirect |
| 36. C8×Dic293 | C22 | semidirect |
| 63. C2×#14556873 | D4 | semidirect |
| 86. M16×C293 | D4 | semidirect |
| 148. C293 | #3154 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D293 | semidirect |
| 226. M16 | C22⋊D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627657 | 2 |
| C2×#22627644 | 2 |
| C22×#17989790 | 2 |
| #34036700 | 2 |
| #34036696 | 2 |
| #34036520 | 2 |
| #34036517 | 2 |
| #34036512 | 2 |
| #34036500 | 2 |
| #34036087 | 2 |
| C2×AGL(1,ℤ/8)×C293 | 2 |
| #3154 | 293 |