Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
588 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 82 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. #34037127 | C2 | semidirect |
| 2. #34037121 | C2 | semidirect |
| 3. #34037115 | C2 | semidirect |
| 4. #34037108 | C2 | semidirect |
| 6. D293⋊M16 | C22 | semidirect |
| 7. #22627703 | C22 | semidirect |
| 16. C2×#17989802 | C4 | semidirect |
| 19. C2×#17989801 | C4 | semidirect |
| 24. C2×D4×D293 | C4 | semidirect |
| 26. C22×D4×C293 | C4 | semidirect |
| 151. C293 | #1795 | semidirect |
| 170. C22×D4 | #11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037127 | 2 |
| #34037121 | 2 |
| #34037115 | 2 |
| #34037108 | 2 |
| C2×#22627669 | 2 |
| #1795 | 293 |