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. #34036674 | C2 | semidirect |
| 2. #34036533 | C2 | semidirect |
| 3. #34036504 | C2 | semidirect |
| 4. #34036474 | C2 | semidirect |
| 5. #34036365 | C2 | semidirect |
| 6. #34036363 | C2 | semidirect |
| 7. D8×Dic293 | C2 | semidirect |
| 8. #34036211 | C2 | semidirect |
| 9. #34036209 | C2 | semidirect |
| 10. C2×C8×Dic293 | C2 | semidirect |
| 11. #466×C293 | C2 | semidirect |
| 82. C2×Dic293 | D8 | semidirect |
| 89. #14556873 | #41 | semidirect |
| 101. C8×C293 | #41 | semidirect |
| 127. C293 | #3169 | semidirect |
| 135. #466 | D293 | semidirect |
| 229. C8 | #17989801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036674 | 2 |
| #34036533 | 2 |
| #34036504 | 2 |
| #34036474 | 2 |
| #34036365 | 2 |
| #34036363 | 2 |
| D8×Dic293 | 2 |
| #34036211 | 2 |
| #34036209 | 2 |
| C2×C8×Dic293 | 2 |
| #466×C293 | 2 |
| #3169 | 293 |