Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
928 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 237 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×C4×D116 | C2 | semidirect |
| 3. #14271069 | C2 | semidirect |
| 4. #14271039 | C2 | semidirect |
| 5. #14271025 | C2 | semidirect |
| 6. #14271023 | C2 | semidirect |
| 7. #95×D29 | C2 | semidirect |
| 8. C4×C22⋊C4×C29 | C2 | semidirect |
| 12. C2×#90805 | C4 | semidirect |
| 31. C22×C4×C29 | C2×C4 | semidirect |
| 37. C2×C22⋊D29 | C2×C4 | semidirect |
| 47. C2×C4×D29 | C2×C4 | semidirect |
| 49. C2×Dic58 | C2×C4 | semidirect |
| 76. C2×C4×C29 | #41 | semidirect |
| 83. D116 | C22⋊C4 | semidirect |
| 115. C4×C22⋊C4 | D29 | semidirect |
| 143. C29 | #2339 | semidirect |
| 161. C22×C4 | C4×D29 | semidirect |
| 201. 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×C4×D116 | 2 |
| #14271069 | 2 |
| #14271039 | 2 |
| #14271025 | 2 |
| #14271023 | 2 |
| #95×D29 | 2 |
| C4×C22⋊C4×C29 | 2 |
| #2339 | 29 |