Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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×#11745250 | C2 | semidirect |
| 3. #14271451 | C2 | direct (N × H) |
| 4. C2×#11745165 | C2 | semidirect |
| 5. C2×#11745156 | C2 | semidirect |
| 6. C2×#11745162 | C2 | semidirect |
| 23. #11745250 | C22 | semidirect |
| 26. #11745165 | C22 | semidirect |
| 27. #11745162 | C22 | semidirect |
| 28. #11745156 | C22 | semidirect |
| 32. C2×D4×C29 | Q8 | semidirect |
| 65. D4×C29 | C2×Q8 | semidirect |
| 110. C2×C29 | #476 | semidirect |
| 134. C29 | C2×#476 | semidirect |
| 140. C2×D4 | Dic58 | semidirect |
| 172. D4 | C2×Dic58 | semidirect |
| 207. C2 | #14271451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745250 | 2 |
| C2×D4×Dic29 | 2 |
| #14271451 | 2 |
| C2×#11745165 | 2 |
| C2×#11745156 | 2 |
| C2×#11745162 | 2 |
| C2×#11745180 | 2 |
| C2×C29×#102 | 2 |
| C2×#476 | 29 |