Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 160 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. #14272230 | C2 | semidirect |
| 2. #14272204 | C2 | semidirect |
| 3. D8×#1181 | C2 | semidirect |
| 4. #14272173 | C2 | semidirect |
| 5. #14272155 | C2 | semidirect |
| 6. #14272126 | C2 | semidirect |
| 11. D4×#1181 | C22 | semidirect |
| 15. C2×D8×C29 | C4 | semidirect |
| 16. C2×#90782 | C4 | semidirect |
| 17. D8×D29 | C4 | semidirect |
| 18. D8×D29 | C4 | semidirect |
| 21. C2×D232 | C4 | semidirect |
| 23. #11745223 | C22 | semidirect |
| 24. #11745210 | C22 | semidirect |
| 25. #11745209 | C22 | semidirect |
| 26. #11745208 | C22 | semidirect |
| 27. C8×#1181 | C22 | semidirect |
| 30. C2×D4×C29 | C2×C4 | semidirect |
| 34. D4×D29 | C2×C4 | semidirect |
| 36. C2×D116 | C2×C4 | semidirect |
| 48. D8×C29 | C2×C4 | semidirect |
| 49. D8×C29 | C2×C4 | semidirect |
| 50. C2×C8×C29 | C2×C4 | semidirect |
| 51. #90782 | C2×C4 | semidirect |
| 52. #90782 | C2×C4 | semidirect |
| 53. C2×#6597 | C2×C4 | semidirect |
| 54. D232 | C2×C4 | semidirect |
| 55. D232 | C2×C4 | semidirect |
| 56. C8×D29 | C2×C4 | semidirect |
| 57. C8×D29 | C2×C4 | semidirect |
| 123. C2×D8 | #1181 | semidirect |
| 136. C29 | #2948 | semidirect |
| 144. C2×D4 | C2×#1181 | semidirect |
| 151. D8 | C2×#1181 | semidirect |
| 152. D8 | C2×#1181 | semidirect |
| 161. C2×C8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272230 | 2 |
| #14272204 | 2 |
| D8×#1181 | 2 |
| #14272173 | 2 |
| #14272155 | 2 |
| #14272126 | 2 |
| C2×D8×D29 | 2 |
| #2948 | 29 |