Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
300 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 70 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×#22627694 | C2 | semidirect |
| 2. C2×#22627689 | C2 | semidirect |
| 3. C2×#22627688 | C2 | semidirect |
| 4. #34037104 | C2 | semidirect |
| 5. #34037103 | C2 | semidirect |
| 6. C2×C8×#11924078 | C2 | semidirect |
| 22. C2×#17989792 | C4 | semidirect |
| 23. C2×#17989791 | C4 | semidirect |
| 24. C2×#17989787 | C4 | semidirect |
| 26. C2×SD16×C293 | C4 | semidirect |
| 119. C293 | #1974 | semidirect |
| 134. C2×SD16 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627694 | 2 |
| C2×#22627689 | 2 |
| C2×#22627688 | 2 |
| #34037104 | 2 |
| #34037103 | 2 |
| C2×C8×#11924078 | 2 |
| C2×#22627645 | 2 |
| #1974 | 293 |