Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 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. #34036757 | C2 | semidirect |
| 2. #34036429 | C2 | semidirect |
| 3. #34036429 | C2 | semidirect |
| 4. #34036419 | C2 | semidirect |
| 5. #34036409 | C2 | semidirect |
| 6. #34036172 | C2 | semidirect |
| 7. #34036165 | C2 | semidirect |
| 8. #34036156 | C2 | semidirect |
| 14. #22627624 | C22 | semidirect |
| 16. #22627616 | C22 | semidirect |
| 21. #22627557 | C22 | semidirect |
| 22. #22627557 | C22 | semidirect |
| 23. #22627557 | C22 | semidirect |
| 24. #22627555 | C22 | semidirect |
| 25. #22627555 | C22 | semidirect |
| 26. #22627555 | C22 | semidirect |
| 27. C4⋊#14556873 | C22 | semidirect |
| 28. C4⋊#14556873 | C22 | semidirect |
| 60. C2×D4×C293 | Q8 | semidirect |
| 124. C293 | #3081 | semidirect |
| 170. C2×D4 | Dic586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036757 | 2 |
| #34036429 | 2 |
| #34036419 | 2 |
| #34036409 | 2 |
| #34036172 | 2 |
| #34036165 | 2 |
| #34036156 | 2 |
| #34036134 | 2 |
| C2×#22627545 | 2 |
| #518×C293 | 2 |
| #3081 | 293 |