Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#11745270 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. C2×C4×D116 | C2 | semidirect |
| 4. #14271379 | C2 | semidirect |
| 5. #14271369 | C2 | semidirect |
| 6. #14271359 | C2 | semidirect |
| 7. #14271165 | C2 | semidirect |
| 8. C29×#423 | C2 | semidirect |
| 21. #11745237 | C22 | semidirect |
| 22. #11745236 | C22 | semidirect |
| 29. #11745231 | C22 | semidirect |
| 30. C29×C4⋊C8 | C22 | semidirect |
| 31. C29×C4⋊C8 | C22 | semidirect |
| 32. #11745169 | C22 | semidirect |
| 33. #11745164 | C22 | semidirect |
| 46. C2×D116 | D4 | semidirect |
| 119. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 130. #423 | D29 | semidirect |
| 159. C4⋊C8 | C2×D29 | semidirect |
| 160. C4⋊C8 | C2×D29 | semidirect |
| 163. C29 | #3036 | semidirect |
| 250. C4 | #11745270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271713 | 2 |
| C2×C4×D116 | 2 |
| #14271379 | 2 |
| #14271369 | 2 |
| #14271359 | 2 |
| #14271165 | 2 |
| C29×#423 | 2 |
| #3036 | 29 |