Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 145 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. #34036686 | C2 | semidirect |
| 2. #34036525 | C2 | semidirect |
| 3. #34036501 | C2 | semidirect |
| 4. #34036481 | C2 | semidirect |
| 5. #34036475 | C2 | semidirect |
| 6. #34036356 | C2 | semidirect |
| 7. C4×#17989790 | C2 | semidirect |
| 8. C2×C4×#14556873 | C2 | semidirect |
| 72. #14556873 | #41 | semidirect |
| 84. C2×C4×C293 | SD16 | semidirect |
| 112. C293 | #3167 | semidirect |
| 195. C2×C4 | #17989790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036686 | 2 |
| #34036525 | 2 |
| #34036501 | 2 |
| #34036481 | 2 |
| #34036475 | 2 |
| #34036356 | 2 |
| C4×#17989790 | 2 |
| C2×C4×#14556873 | 2 |
| #532×C293 | 2 |
| #3167 | 293 |