Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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×#22627646 | C2 | semidirect |
| 2. #34036640 | C2 | semidirect |
| 3. #34036387 | C2 | semidirect |
| 4. #34036382 | C2 | semidirect |
| 5. #34036375 | C2 | semidirect |
| 6. #34036167 | C2 | semidirect |
| 7. #34036126 | C2 | semidirect |
| 8. C22×M16×C293 | C2 | semidirect |
| 11. C2×Dic1172 | C22 | semidirect |
| 12. C2×#17989791 | C22 | semidirect |
| 13. C2×D2344 | C22 | semidirect |
| 20. #22627558 | C22 | semidirect |
| 21. #22627556 | C22 | semidirect |
| 22. #22627549 | C22 | semidirect |
| 23. #22627546 | C22 | semidirect |
| 56. C2×C8×C293 | D4 | semidirect |
| 105. C293 | #3054 | semidirect |
| 108. C22×M16 | D293 | semidirect |
| 156. C2×C8 | C22⋊D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627646 | 2 |
| #34036640 | 2 |
| #34036387 | 2 |
| #34036382 | 2 |
| #34036375 | 2 |
| #34036167 | 2 |
| #34036126 | 2 |
| C22×M16×C293 | 2 |
| #3054 | 293 |