Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#11745215 | C2 | semidirect |
| 2. #14272070 | C2 | semidirect |
| 3. #14272068 | C2 | semidirect |
| 5. C2×#90805 | C4 | semidirect |
| 8. C29×#117 | C4 | semidirect |
| 11. #11745237 | C4 | semidirect |
| 13. #11745236 | C4 | semidirect |
| 26. C2×D116 | C2×C4 | semidirect |
| 30. C2×Dic58 | C2×C4 | semidirect |
| 35. C42×C29 | C2×C4 | semidirect |
| 36. C42×C29 | C2×C4 | semidirect |
| 99. #117 | #1181 | semidirect |
| 103. C29 | #2127 | semidirect |
| 124. C42 | C2×#1181 | semidirect |
| 125. C42 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745215 | 2 |
| #14272070 | 2 |
| #14272068 | 2 |
| #14271732 | 2 |
| #2127 | 29 |