Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 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 |
|---|---|---|
| 3. #34036537 | C2 | semidirect |
| 4. #34036536 | C2 | semidirect |
| 5. #34036530 | C2 | semidirect |
| 6. #34036526 | C2 | semidirect |
| 44. C2×#14556873 | Q8 | semidirect |
| 65. M16×C293 | Q8 | semidirect |
| 112. C293 | #3163 | semidirect |
| 159. M16 | Dic586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036760 | 2 |
| #34036757 | 2 |
| #34036537 | 2 |
| #34036536 | 2 |
| #34036530 | 2 |
| #34036526 | 2 |
| #34036171 | 2 |
| #34036165 | 2 |
| C2×#22627555 | 2 |
| #34036087 | 2 |
| #428×C293 | 2 |
| #3163 | 293 |