Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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×#22627695 | C2 | semidirect |
| 3. #34037136 | C2 | semidirect |
| 5. #34036999 | C2 | semidirect |
| 6. (C2×#11924078)⋊C8 | C2 | semidirect |
| 23. #22627549 | C4 | semidirect |
| 24. #22627547 | C4 | semidirect |
| 25. #22627545 | C4 | semidirect |
| 26. #102×C293 | C4 | semidirect |
| 109. C293 | #1866 | semidirect |
| 136. #102 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627711 | 2 |
| C2×#22627695 | 2 |
| #34037136 | 2 |
| C2×#22627688 | 2 |
| #34036999 | 2 |
| (C2×#11924078)⋊C8 | 2 |
| #34036122 | 2 |
| #1866 | 293 |