Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #14271638 | C2 | semidirect |
| 3. #14271637 | C2 | semidirect |
| 4. #14271272 | C2 | semidirect |
| 5. #14271243 | C2 | semidirect |
| 6. #14271199 | C2 | semidirect |
| 7. #14271169 | C2 | semidirect |
| 8. #14271121 | C2 | semidirect |
| 9. C29×#418 | C2 | semidirect |
| 16. D4×Dic29 | C22 | semidirect |
| 17. C2×#90782 | C4 | semidirect |
| 23. #11745255 | C22 | semidirect |
| 26. C29×#102 | C22 | semidirect |
| 27. #11745169 | C22 | semidirect |
| 28. #11745163 | C22 | semidirect |
| 29. C8×Dic29 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 31. #11745155 | C22 | semidirect |
| 36. C2×D4×C29 | C2×C4 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 53. #90782 | C2×C4 | semidirect |
| 54. #90782 | C2×C4 | semidirect |
| 60. C2×#6597 | C2×C4 | semidirect |
| 111. #418 | D29 | semidirect |
| 137. #102 | C2×D29 | semidirect |
| 140. C29 | #2948 | semidirect |
| 149. C2×D4 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| #14271638 | 2 |
| #14271637 | 2 |
| #14271272 | 2 |
| #14271243 | 2 |
| #14271199 | 2 |
| #14271169 | 2 |
| #14271121 | 2 |
| C29×#418 | 2 |
| #2948 | 29 |