Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22627656 | C2 | semidirect |
| 2. C2×#22627653 | C2 | semidirect |
| 4. C4⋊Q8×D293 | C2 | semidirect |
| 5. #34036524 | C2 | semidirect |
| 6. #34036523 | C2 | semidirect |
| 7. #34036521 | C2 | semidirect |
| 8. #34036507 | C2 | semidirect |
| 9. #34036500 | C2 | semidirect |
| 10. #34036081 | C2 | semidirect |
| 11. #497×C293 | C2 | semidirect |
| 63. #17989785 | D4 | semidirect |
| 124. Dic293 | #137 | semidirect |
| 130. C293 | #3152 | semidirect |
| 139. #497 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627656 | 2 |
| C2×#22627653 | 2 |
| #34036678 | 2 |
| C4⋊Q8×D293 | 2 |
| #34036524 | 2 |
| #34036523 | 2 |
| #34036521 | 2 |
| #34036507 | 2 |
| #34036500 | 2 |
| #34036081 | 2 |
| #497×C293 | 2 |
| #3152 | 293 |