Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#22627589 | C2 | semidirect |
| 4. #34036435 | C2 | semidirect |
| 5. #34036354 | C2 | semidirect |
| 6. #34036284 | C2 | semidirect |
| 8. #34036233 | C2 | semidirect |
| 9. #34036228 | C2 | semidirect |
| 10. #34036183 | C2 | semidirect |
| 11. #484×C293 | C2 | semidirect |
| 131. C293 | #3117 | semidirect |
| 135. #484 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036665 | 2 |
| C2×#22627589 | 2 |
| #34036447 | 2 |
| #34036435 | 2 |
| #34036354 | 2 |
| #34036284 | 2 |
| #34036270 | 2 |
| #34036233 | 2 |
| #34036228 | 2 |
| #34036183 | 2 |
| #484×C293 | 2 |
| #3117 | 293 |