Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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. C2×#22627650 | C2 | semidirect |
| 2. #34036679 | C2 | semidirect |
| 3. #34036344 | C2 | semidirect |
| 4. #34036334 | C2 | semidirect |
| 5. #34036324 | C2 | semidirect |
| 6. #34036153 | C2 | semidirect |
| 7. #34036128 | C2 | semidirect |
| 8. C2×C4×D4×C293 | C2 | semidirect |
| 14. #22627624 | C22 | semidirect |
| 15. #22627621 | C22 | semidirect |
| 16. #22627612 | C22 | semidirect |
| 21. C4⋊#14556873 | C22 | semidirect |
| 22. C4⋊#14556873 | C22 | semidirect |
| 23. #22627547 | C22 | semidirect |
| 24. #22627544 | C22 | semidirect |
| 53. C2×D4×C293 | D4 | semidirect |
| 119. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 129. C293 | #3036 | semidirect |
| 133. C2×C4×D4 | D293 | semidirect |
| 174. C2×D4 | D1172 | semidirect |
| 250. C4 | #22627650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627650 | 2 |
| #34036679 | 2 |
| #34036344 | 2 |
| #34036334 | 2 |
| #34036324 | 2 |
| #34036153 | 2 |
| #34036128 | 2 |
| C2×C4×D4×C293 | 2 |
| #3036 | 293 |