Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22627648 | C2 | semidirect |
| 2. #34036677 | C2 | semidirect |
| 3. C4×D4×D293 | C2 | semidirect |
| 4. #34036343 | C2 | semidirect |
| 5. #34036342 | C2 | semidirect |
| 6. #34036335 | C2 | semidirect |
| 7. #34036334 | C2 | semidirect |
| 8. #34036321 | C2 | semidirect |
| 9. #34036151 | C2 | semidirect |
| 10. #34036127 | C2 | semidirect |
| 11. #459×C293 | C2 | semidirect |
| 20. #22627624 | C22 | semidirect |
| 21. #22627611 | C22 | semidirect |
| 34. C4⋊#14556873 | C22 | semidirect |
| 35. #22627553 | C22 | semidirect |
| 36. #22627549 | C22 | semidirect |
| 37. #22627547 | C22 | semidirect |
| 38. #22627545 | C22 | semidirect |
| 40. #127×C293 | C22 | semidirect |
| 42. C4⋊C8×C293 | C22 | semidirect |
| 43. #102×C293 | C22 | semidirect |
| 52. D4×D293 | D4 | semidirect |
| 145. C4×C293 | AGL(1,ℤ/8) | semidirect |
| 160. C293 | #3036 | semidirect |
| 170. #459 | D293 | semidirect |
| 183. #127 | C2×D293 | semidirect |
| 200. C4⋊C8 | C2×D293 | semidirect |
| 204. #102 | C2×D293 | semidirect |
| 311. C4 | #22627648 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22627648 | 2 |
| #34036677 | 2 |
| C4×D4×D293 | 2 |
| #34036343 | 2 |
| #34036342 | 2 |
| #34036335 | 2 |
| #34036334 | 2 |
| #34036321 | 2 |
| #34036151 | 2 |
| #34036127 | 2 |
| #459×C293 | 2 |
| #3036 | 293 |