Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D1172 | C2 | semidirect |
| 3. #34036480 | C2 | semidirect |
| 4. #34036461 | C2 | semidirect |
| 5. #34036414 | C2 | semidirect |
| 6. #34036357 | C2 | semidirect |
| 7. #34036334 | C2 | semidirect |
| 8. #34036266 | C2 | semidirect |
| 9. C8×D1172 | C2 | semidirect |
| 10. #103×D293 | C2 | semidirect |
| 11. C4×SD16×C293 | C2 | semidirect |
| 82. D1172 | SD16 | semidirect |
| 94. Q8×C293 | #41 | semidirect |
| 128. C293 | #3298 | semidirect |
| 138. C4×SD16 | D293 | semidirect |
| 213. Q8 | #17989802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1172 | 2 |
| #34036784 | 2 |
| #34036480 | 2 |
| #34036461 | 2 |
| #34036414 | 2 |
| #34036357 | 2 |
| #34036334 | 2 |
| #34036266 | 2 |
| C8×D1172 | 2 |
| #103×D293 | 2 |
| C4×SD16×C293 | 2 |
| #3298 | 293 |