Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
222 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 60 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. #34037136 | C2 | semidirect |
| 4. C2×#22627678 | C2 | semidirect |
| 5. #34037005 | C2 | semidirect |
| 6. #34036999 | C2 | semidirect |
| 21. #22627549 | C4 | semidirect |
| 22. #22627547 | C4 | semidirect |
| 23. #22627545 | C4 | semidirect |
| 24. #102×C293 | C4 | semidirect |
| 105. C293 | #1938 | semidirect |
| 127. #102 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037136 | 2 |
| C2×#22627688 | 2 |
| #34037103 | 2 |
| C2×#22627678 | 2 |
| #34037005 | 2 |
| #34036999 | 2 |
| #34036122 | 2 |
| #1938 | 293 |