Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
174 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 90 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. C22×#17989805 | C2 | semidirect |
| 2. C4⋊#17989805 | C2 | semidirect |
| 3. C22⋊#17989805 | C2 | semidirect |
| 4. C4×#17989805 | C2 | semidirect |
| 17. #17989805 | D4 | direct (N × H) |
| 33. D4×C293 | C16 | semidirect |
| 42. C22×C293 | C2×C16 | semidirect |
| 46. C4×C293 | C2×C16 | semidirect |
| 53. C293 | D4×C16 | semidirect |
| 83. D4 | #17989805 | direct (N × H) |
| 96. C22 | C2×#17989805 | semidirect |
| 100. C4 | C2×#17989805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17989805 | 2 |
| C4⋊#17989805 | 2 |
| C22⋊#17989805 | 2 |
| C4×#17989805 | 2 |
| D4×#14556873 | 2 |
| D4×C16 | 293 |