Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 1. C2×#22627623 | C2 | semidirect |
| 3. #34036423 | C2 | semidirect |
| 4. #34036418 | C2 | semidirect |
| 5. #34036413 | C2 | semidirect |
| 6. #34036408 | C2 | semidirect |
| 7. #34036172 | C2 | semidirect |
| 8. #34036152 | C2 | semidirect |
| 11. #428×C293 | C2 | semidirect |
| 44. #17989802 | Q8 | semidirect |
| 87. Dic586 | C2×Q8 | semidirect |
| 89. D1172 | C2×Q8 | semidirect |
| 138. C293 | #3079 | semidirect |
| 147. #428 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627623 | 2 |
| #34036597 | 2 |
| #34036423 | 2 |
| #34036418 | 2 |
| #34036413 | 2 |
| #34036408 | 2 |
| #34036172 | 2 |
| #34036152 | 2 |
| #34036131 | 2 |
| #34036128 | 2 |
| #428×C293 | 2 |
| #3079 | 293 |