Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
456 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 173 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. #34036024 | C2 | semidirect |
| 4. #34036010 | C2 | semidirect |
| 6. #34035997 | C2 | semidirect |
| 7. #384×C293 | C2 | semidirect |
| 9. #22627618 | C4 | semidirect |
| 28. #17989781 | C2×C4 | semidirect |
| 37. C42×C293 | C2×C4 | semidirect |
| 72. C293 | #2383 | semidirect |
| 79. #384 | D293 | semidirect |
| 110. C42 | C4×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627618 | 2 |
| #34036024 | 2 |
| #34036019 | 2 |
| #34036010 | 2 |
| #34036000 | 2 |
| #34035997 | 2 |
| #384×C293 | 2 |
| #2383 | 293 |