Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 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. #41×Dic29 | C2 | semidirect |
| 3. C2×#11745173 | C2 | semidirect |
| 4. #14271136 | C2 | semidirect |
| 5. #14270934 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×#421 | C2 | semidirect |
| 12. #11745313 | C4 | semidirect |
| 14. #11745311 | C4 | semidirect |
| 45. C2×D116 | C2×C4 | semidirect |
| 47. C2×Dic58 | C2×C4 | semidirect |
| 68. #90777 | C2×C4 | semidirect |
| 126. #421 | D29 | semidirect |
| 158. C29 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271961 | 2 |
| #41×Dic29 | 2 |
| C2×#11745173 | 2 |
| #14271136 | 2 |
| #14270934 | 2 |
| #14270922 | 2 |
| C29×#421 | 2 |
| #1906 | 29 |