Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
516 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 168 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. #34037078 | C2 | semidirect |
| 3. #34037074 | C2 | semidirect |
| 4. C4⋊C4×#11924078 | C2 | semidirect |
| 6. C42×#11924078 | C2 | semidirect |
| 18. #22627619 | C4 | semidirect |
| 19. #22627618 | C4 | semidirect |
| 20. #22627617 | C4 | semidirect |
| 24. #126×C293 | C4 | semidirect |
| 38. C4⋊Dic293 | C2×C4 | semidirect |
| 39. #17989781 | C2×C4 | semidirect |
| 40. #17989781 | C2×C4 | semidirect |
| 44. C4×Dic293 | C2×C4 | semidirect |
| 45. C4⋊C4×C293 | C2×C4 | semidirect |
| 47. C42×C293 | C2×C4 | semidirect |
| 80. #11924078 | #126 | direct (N × H) |
| 90. C293 | C4×#126 | semidirect |
| 103. #126 | #11924078 | direct (N × H) |
| 128. C4⋊C4 | C2×#11924078 | semidirect |
| 138. C42 | C2×#11924078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34037079 | 2 |
| #34037078 | 2 |
| #34037074 | 2 |
| C4⋊C4×#11924078 | 2 |
| C22⋊C4×#11924078 | 2 |
| C42×#11924078 | 2 |
| #126×D293 | 2 |
| C4×#126 | 293 |