Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #34036760 | C2 | semidirect |
| 3. #34036431 | C2 | semidirect |
| 4. #34036427 | C2 | semidirect |
| 5. #34036417 | C2 | semidirect |
| 6. #34036407 | C2 | semidirect |
| 7. #34036169 | C2 | semidirect |
| 8. #34036167 | C2 | semidirect |
| 9. #34036155 | C2 | semidirect |
| 14. #22627623 | C22 | semidirect |
| 16. #22627615 | C22 | semidirect |
| 26. #22627558 | C22 | semidirect |
| 27. #22627558 | C22 | semidirect |
| 28. #22627557 | C22 | semidirect |
| 29. #22627556 | C22 | semidirect |
| 30. #22627556 | C22 | semidirect |
| 31. #22627555 | C22 | semidirect |
| 32. #22627553 | C22 | semidirect |
| 33. #22627553 | C22 | semidirect |
| 66. 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 |
|---|---|
| #34036760 | 2 |
| #34036604 | 2 |
| #34036431 | 2 |
| #34036427 | 2 |
| #34036417 | 2 |
| #34036407 | 2 |
| #34036169 | 2 |
| #34036167 | 2 |
| #34036155 | 2 |
| #34036134 | 2 |
| C2×#102×C293 | 2 |
| #3081 | 293 |