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. #34036481 | C2 | semidirect |
| 4. #34036461 | C2 | semidirect |
| 5. #34036359 | C2 | semidirect |
| 6. #34036335 | C2 | semidirect |
| 7. #34036269 | C2 | semidirect |
| 8. C4×#17989789 | C2 | semidirect |
| 9. #34036194 | C2 | semidirect |
| 10. #103×D293 | C2 | semidirect |
| 11. #475×C293 | C2 | semidirect |
| 85. D1172 | SD16 | semidirect |
| 98. Q8×C293 | #41 | semidirect |
| 128. C293 | #3298 | semidirect |
| 134. #475 | D293 | semidirect |
| 213. Q8 | #17989803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D1172 | 2 |
| #34036782 | 2 |
| #34036481 | 2 |
| #34036461 | 2 |
| #34036359 | 2 |
| #34036335 | 2 |
| #34036269 | 2 |
| C4×#17989789 | 2 |
| #34036194 | 2 |
| #103×D293 | 2 |
| #475×C293 | 2 |
| #3298 | 293 |