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. #34036026 | C2 | semidirect |
| 4. #34036016 | C2 | semidirect |
| 6. #34035999 | C2 | semidirect |
| 7. #383×C293 | C2 | semidirect |
| 9. #22627618 | C4 | semidirect |
| 30. #17989781 | C2×C4 | semidirect |
| 37. C42×C293 | C2×C4 | semidirect |
| 72. C293 | #2383 | semidirect |
| 80. #383 | 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 |
| #34036026 | 2 |
| #34036021 | 2 |
| #34036016 | 2 |
| #34036003 | 2 |
| #34035999 | 2 |
| #383×C293 | 2 |
| #2383 | 293 |