Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 1. #34036676 | C2 | semidirect |
| 2. #34036533 | C2 | semidirect |
| 3. #34036504 | C2 | semidirect |
| 4. #34036474 | C2 | semidirect |
| 5. #34036366 | C2 | semidirect |
| 6. #34036364 | C2 | semidirect |
| 7. #34036362 | C2 | semidirect |
| 8. C4×D2344 | C2 | semidirect |
| 9. C4×#17989787 | C2 | semidirect |
| 10. C4×C8×D293 | C2 | semidirect |
| 11. C4×D8×C293 | C2 | semidirect |
| 89. C4×D293 | D8 | semidirect |
| 91. #14556873 | #41 | semidirect |
| 101. C8×C293 | #41 | semidirect |
| 127. C293 | #3169 | semidirect |
| 138. C4×D8 | D293 | semidirect |
| 229. C8 | #17989802 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036676 | 2 |
| #34036533 | 2 |
| #34036504 | 2 |
| #34036474 | 2 |
| #34036366 | 2 |
| #34036364 | 2 |
| #34036362 | 2 |
| C4×D2344 | 2 |
| C4×#17989787 | 2 |
| C4×C8×D293 | 2 |
| C4×D8×C293 | 2 |
| #3169 | 293 |