Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×#17989785 | C2 | semidirect |
| 3. C2×C4⋊C4×D293 | C2 | semidirect |
| 4. #34036129 | C2 | direct (N × H) |
| 5. C2×#22627548 | C2 | semidirect |
| 6. C2×#22627546 | C2 | semidirect |
| 7. C2×#22627544 | C2 | semidirect |
| 8. C2×#103×C293 | C2 | semidirect |
| 11. C2×#17989803 | C4 | semidirect |
| 19. C2×#17989785 | C22 | semidirect |
| 24. C4⋊C4×D293 | C22 | semidirect |
| 25. #22627548 | C22 | semidirect |
| 26. #22627546 | C22 | semidirect |
| 27. #22627544 | C22 | semidirect |
| 31. #103×C293 | C22 | semidirect |
| 36. #17989803 | C2×C4 | semidirect |
| 41. C2×D1172 | C2×C4 | semidirect |
| 61. C2×Q8×C293 | C2×C4 | semidirect |
| 81. D1172 | C22×C4 | semidirect |
| 95. Q8×C293 | C22×C4 | semidirect |
| 124. C2×C293 | #417 | semidirect |
| 130. C293 | C2×#417 | semidirect |
| 137. C2×#103 | D293 | semidirect |
| 160. #103 | C2×D293 | semidirect |
| 170. C2×Q8 | C4×D293 | semidirect |
| 212. Q8 | C2×C4×D293 | semidirect |
| 257. C2 | #34036129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#17989803 | 2 |
| C22×#17989785 | 2 |
| C2×C4⋊C4×D293 | 2 |
| #34036129 | 2 |
| C2×#22627548 | 2 |
| C2×#22627546 | 2 |
| C2×#22627544 | 2 |
| C2×#103×C293 | 2 |
| C2×#417 | 293 |