Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
544 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22627624 | C2 | semidirect |
| 3. #34036334 | C2 | direct (N × H) |
| 4. C2×C4⋊#14556873 | C2 | semidirect |
| 5. C2×#22627547 | C2 | semidirect |
| 12. #22627624 | C22 | semidirect |
| 15. C4⋊#14556873 | C22 | semidirect |
| 16. #22627547 | C22 | semidirect |
| 68. C2×C4×C293 | SD16 | semidirect |
| 86. C4×C293 | C2×SD16 | semidirect |
| 91. C2×C293 | #461 | semidirect |
| 95. C293 | C2×#461 | semidirect |
| 163. C2×C4 | #17989790 | semidirect |
| 183. C4 | C2×#17989790 | semidirect |
| 187. C2 | #34036334 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17989790 | 2 |
| C2×#22627624 | 2 |
| #34036334 | 2 |
| C2×C4⋊#14556873 | 2 |
| C2×#22627547 | 2 |
| C2×C4×D4×C293 | 2 |
| C2×#461 | 293 |