Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
936 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 285 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. C2×#11745288 | C2 | semidirect |
| 3. #14271069 | C2 | semidirect |
| 4. #14271065 | C2 | semidirect |
| 5. #14271042 | C2 | semidirect |
| 6. C4×#90781 | C2 | semidirect |
| 7. C22×C42×C29 | C2 | semidirect |
| 13. C2×#90805 | C4 | semidirect |
| 44. C2×D116 | C2×C4 | semidirect |
| 47. C2×C4×D29 | C2×C4 | semidirect |
| 50. C2×Dic58 | C2×C4 | semidirect |
| 69. C2×C4×C29 | C22⋊C4 | semidirect |
| 76. C2×C4×C29 | #41 | semidirect |
| 106. C22×C42 | D29 | semidirect |
| 135. C29 | #2297 | semidirect |
| 188. C2×C4 | #90781 | semidirect |
| 193. C2×C4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90805 | 2 |
| C2×#11745288 | 2 |
| #14271069 | 2 |
| #14271065 | 2 |
| #14271042 | 2 |
| C4×#90781 | 2 |
| C22×C42×C29 | 2 |
| #2297 | 29 |