Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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×#22627678 | C2 | semidirect |
| 4. #34037080 | C2 | semidirect |
| 5. #34037003 | C2 | semidirect |
| 6. #34037002 | C2 | semidirect |
| 21. #22627546 | C4 | semidirect |
| 22. #22627545 | C4 | semidirect |
| 23. #22627544 | C4 | semidirect |
| 24. #102×C293 | C4 | semidirect |
| 134. C293 | #1936 | semidirect |
| 157. #102 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627686 | 2 |
| C2×#22627678 | 2 |
| #34037081 | 2 |
| #34037080 | 2 |
| #34037003 | 2 |
| #34037002 | 2 |
| #102×D293 | 2 |
| #1936 | 293 |