Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#22627671 | C2 | semidirect |
| 2. #34036927 | C2 | semidirect |
| 3. #34036700 | C2 | semidirect |
| 4. #34036310 | C2 | semidirect |
| 5. #34036300 | C2 | semidirect |
| 6. #34036146 | C2 | semidirect |
| 7. #34036145 | C2 | semidirect |
| 8. C2×#22627542 | C2 | semidirect |
| 9. #575×C293 | C2 | semidirect |
| 21. #22627655 | C22 | semidirect |
| 23. #22627650 | C22 | semidirect |
| 27. #22627622 | C22 | semidirect |
| 28. #22627611 | C22 | semidirect |
| 32. #22627551 | C22 | semidirect |
| 33. #22627550 | C22 | semidirect |
| 34. #22627542 | C22 | semidirect |
| 38. #137×C293 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C293 | C22 | semidirect |
| 185. C293 | #3020 | semidirect |
| 189. #575 | D293 | semidirect |
| 212. #137 | C2×D293 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627671 | 2 |
| #34036927 | 2 |
| #34036700 | 2 |
| #34036310 | 2 |
| #34036300 | 2 |
| #34036146 | 2 |
| #34036145 | 2 |
| C2×#22627542 | 2 |
| #575×C293 | 2 |
| #3020 | 293 |