Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. #34036537 | C2 | semidirect |
| 3. #34036535 | C2 | semidirect |
| 4. #34036533 | C2 | semidirect |
| 5. #34036531 | C2 | semidirect |
| 6. #34036530 | C2 | semidirect |
| 11. #500×C293 | C2 | semidirect |
| 42. #17989785 | Q8 | semidirect |
| 45. C8×D293 | Q8 | semidirect |
| 107. C293 | #3164 | semidirect |
| 113. #500 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036756 | 2 |
| #34036537 | 2 |
| #34036535 | 2 |
| #34036533 | 2 |
| #34036531 | 2 |
| #34036530 | 2 |
| #34036170 | 2 |
| #34036166 | 2 |
| #107×D293 | 2 |
| #34036083 | 2 |
| #500×C293 | 2 |
| #3164 | 293 |