Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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. #34036864 | C2 | semidirect |
| 2. #34036486 | C2 | semidirect |
| 3. #34036477 | C2 | semidirect |
| 4. #34036426 | C2 | semidirect |
| 5. #34036421 | C2 | semidirect |
| 6. #34036344 | C2 | semidirect |
| 8. Q8×#14556873 | C2 | semidirect |
| 9. C4×#17989790 | C2 | semidirect |
| 10. C4×#17989787 | C2 | semidirect |
| 11. #554×C293 | C2 | semidirect |
| 122. C293 | #3361 | semidirect |
| 125. #554 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036864 | 2 |
| #34036486 | 2 |
| #34036477 | 2 |
| #34036426 | 2 |
| #34036421 | 2 |
| #34036344 | 2 |
| #34036324 | 2 |
| Q8×#14556873 | 2 |
| C4×#17989790 | 2 |
| C4×#17989787 | 2 |
| #554×C293 | 2 |
| #3361 | 293 |