Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #14272242 | C2 | semidirect |
| 2. #41×#1181 | C2 | semidirect |
| 3. #14272162 | C2 | semidirect |
| 4. #14272160 | C2 | semidirect |
| 5. C2×#11745226 | C2 | semidirect |
| 6. D29⋊#104 | C2 | semidirect |
| 8. C29×2−1+4 | C4 | semidirect |
| 10. #11745364 | C4 | semidirect |
| 11. #11745364 | C4 | semidirect |
| 16. #11745362 | C4 | semidirect |
| 23. #11745345 | C22 | semidirect |
| 24. C2×C4×#1181 | C22 | semidirect |
| 25. D29⋊M16 | C22 | semidirect |
| 26. C2×#90796 | C22 | semidirect |
| 27. #11745226 | C22 | semidirect |
| 28. #11745226 | C22 | semidirect |
| 29. #11745226 | C22 | semidirect |
| 30. #11745224 | C22 | semidirect |
| 31. #11745224 | C22 | semidirect |
| 35. #41×C29 | C2×C4 | semidirect |
| 37. C2×Q8×C29 | C2×C4 | semidirect |
| 42. #90809 | C2×C4 | semidirect |
| 46. Q8×D29 | C2×C4 | semidirect |
| 54. D4×D29 | C2×C4 | semidirect |
| 60. #90805 | C2×C4 | semidirect |
| 63. C2×D116 | C2×C4 | semidirect |
| 149. 2−1+4 | #1181 | semidirect |
| 171. C29 | #2901 | semidirect |
| 189. #41 | C2×#1181 | semidirect |
| 194. C2×Q8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272242 | 2 |
| #41×#1181 | 2 |
| #14272162 | 2 |
| #14272160 | 2 |
| C2×#11745226 | 2 |
| D29⋊#104 | 2 |
| #14272000 | 2 |
| #2901 | 29 |