Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22627655 | C2 | semidirect |
| 2. C2×#22627654 | C2 | semidirect |
| 4. C22×#17989792 | C2 | semidirect |
| 5. #34036705 | C2 | semidirect |
| 6. #34036524 | C2 | semidirect |
| 7. #34036521 | C2 | semidirect |
| 8. #34036511 | C2 | semidirect |
| 9. #34036508 | C2 | semidirect |
| 10. #34036085 | C2 | semidirect |
| 11. #536×C293 | C2 | semidirect |
| 143. C293 | #3156 | semidirect |
| 150. #536 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627655 | 2 |
| C2×#22627654 | 2 |
| C2×#22627644 | 2 |
| C22×#17989792 | 2 |
| #34036705 | 2 |
| #34036524 | 2 |
| #34036521 | 2 |
| #34036511 | 2 |
| #34036508 | 2 |
| #34036085 | 2 |
| #536×C293 | 2 |
| #3156 | 293 |