Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 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×#22627624 | C2 | semidirect |
| 3. #34036425 | C2 | semidirect |
| 4. #34036420 | C2 | semidirect |
| 5. #34036415 | C2 | semidirect |
| 6. #34036410 | C2 | semidirect |
| 7. #34036171 | C2 | semidirect |
| 9. #423×C293 | C2 | semidirect |
| 36. #17989802 | Q8 | semidirect |
| 74. Dic586 | C2×Q8 | semidirect |
| 76. D1172 | C2×Q8 | semidirect |
| 121. C293 | #3079 | semidirect |
| 130. #423 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627624 | 2 |
| C4×#17989802 | 2 |
| #34036425 | 2 |
| #34036420 | 2 |
| #34036415 | 2 |
| #34036410 | 2 |
| #34036171 | 2 |
| #34036131 | 2 |
| #423×C293 | 2 |
| #3079 | 293 |