Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
488 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 121 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. #34036680 | C2 | semidirect |
| 2. C4×D4×D293 | C2 | semidirect |
| 3. #34036449 | C2 | semidirect |
| 4. #34036416 | C2 | semidirect |
| 5. #34036325 | C2 | semidirect |
| 6. #34036324 | C2 | semidirect |
| 7. #34036264 | C2 | semidirect |
| 8. #34036240 | C2 | semidirect |
| 9. #34036238 | C2 | semidirect |
| 10. #34036185 | C2 | semidirect |
| 11. #476×C293 | C2 | semidirect |
| 17. #22627621 | C22 | semidirect |
| 25. #22627586 | C22 | semidirect |
| 31. #22627555 | C22 | semidirect |
| 32. C4⋊#14556873 | C22 | semidirect |
| 33. #22627546 | C22 | semidirect |
| 35. #22627544 | C22 | semidirect |
| 37. #22627534 | C22 | semidirect |
| 38. C4⋊Q8×C293 | C22 | semidirect |
| 40. #106×C293 | C22 | semidirect |
| 41. C4⋊C8×C293 | C22 | semidirect |
| 96. D1172 | #41 | semidirect |
| 115. D4×C293 | #41 | semidirect |
| 154. C293 | #3109 | semidirect |
| 160. #476 | D293 | semidirect |
| 172. C4⋊Q8 | C2×D293 | semidirect |
| 189. #106 | C2×D293 | semidirect |
| 191. C4⋊C8 | C2×D293 | semidirect |
| 256. D4 | #17989803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #34036680 | 2 |
| C4×D4×D293 | 2 |
| #34036449 | 2 |
| #34036416 | 2 |
| #34036325 | 2 |
| #34036324 | 2 |
| #34036264 | 2 |
| #34036240 | 2 |
| #34036238 | 2 |
| #34036185 | 2 |
| #476×C293 | 2 |
| #3109 | 293 |