Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #34036462 | C2 | semidirect |
| 3. #34036406 | C2 | semidirect |
| 4. #34036331 | C2 | semidirect |
| 6. #34036227 | C2 | semidirect |
| 7. #34036186 | C2 | semidirect |
| 8. #533×C293 | C2 | semidirect |
| 18. #22627557 | C22 | semidirect |
| 19. C4⋊#14556873 | C22 | semidirect |
| 20. #22627548 | C22 | semidirect |
| 23. #22627535 | C22 | semidirect |
| 24. C4⋊Q8×C293 | C22 | semidirect |
| 25. C4⋊Q8×C293 | C22 | semidirect |
| 30. C4×Q8×C293 | C22 | semidirect |
| 112. C293 | #3110 | semidirect |
| 114. #533 | D293 | semidirect |
| 125. C4⋊Q8 | C2×D293 | semidirect |
| 126. C4⋊Q8 | C2×D293 | semidirect |
| 131. C4×Q8 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D1172 | 2 |
| #34036462 | 2 |
| #34036406 | 2 |
| #34036331 | 2 |
| #34036279 | 2 |
| #34036227 | 2 |
| #34036186 | 2 |
| #533×C293 | 2 |
| #3110 | 293 |