Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #34036491 | C2 | semidirect |
| 3. #34036486 | C2 | semidirect |
| 4. #34036137 | C2 | semidirect |
| 6. C4×#17989786 | C2 | semidirect |
| 7. #533×C293 | C2 | semidirect |
| 15. #22627547 | C22 | semidirect |
| 17. #22627535 | C22 | semidirect |
| 18. C4×#14556873 | C22 | semidirect |
| 19. C4⋊Q8×C293 | C22 | semidirect |
| 20. #125×C293 | C22 | semidirect |
| 83. C293 | #3140 | semidirect |
| 85. #533 | D293 | semidirect |
| 95. C4⋊Q8 | C2×D293 | semidirect |
| 96. #125 | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627612 | 2 |
| #34036491 | 2 |
| #34036486 | 2 |
| #34036137 | 2 |
| #34036133 | 2 |
| C4×#17989786 | 2 |
| #533×C293 | 2 |
| #3140 | 293 |