Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #14271640 | C2 | semidirect |
| 4. #14271265 | C2 | semidirect |
| 5. C4×#90773 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271173 | C2 | semidirect |
| 9. C29×#405 | C2 | semidirect |
| 17. C2×#90773 | C4 | semidirect |
| 25. C4×Dic58 | C22 | semidirect |
| 26. C29×#97 | C22 | semidirect |
| 27. C4×C8×C29 | C22 | semidirect |
| 29. #11745166 | C22 | semidirect |
| 30. #11745165 | C22 | semidirect |
| 31. #11745164 | C22 | semidirect |
| 42. C2×Dic58 | C2×C4 | semidirect |
| 45. C2×C8×C29 | C2×C4 | semidirect |
| 61. #90773 | C2×C4 | semidirect |
| 62. #90773 | C2×C4 | semidirect |
| 108. #405 | D29 | semidirect |
| 133. #97 | C2×D29 | semidirect |
| 134. C4×C8 | C2×D29 | semidirect |
| 135. C29 | #2949 | semidirect |
| 151. C2×C8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| #14271640 | 2 |
| #14271637 | 2 |
| #14271265 | 2 |
| C4×#90773 | 2 |
| #14271201 | 2 |
| #14271173 | 2 |
| #14271169 | 2 |
| C29×#405 | 2 |
| #2949 | 29 |