Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #14271631 | C2 | semidirect |
| 3. #14271179 | C2 | semidirect |
| 4. C2×#11745173 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. #14270924 | C2 | semidirect |
| 7. C29×#344 | C2 | semidirect |
| 16. #11745271 | C4 | semidirect |
| 18. #11745270 | C4 | semidirect |
| 41. C2×D116 | C2×C4 | semidirect |
| 46. C2×Dic58 | C2×C4 | semidirect |
| 51. M16×C29 | C2×C4 | semidirect |
| 129. #344 | D29 | semidirect |
| 158. C29 | #1906 | semidirect |
| 185. M16 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271963 | 2 |
| #14271631 | 2 |
| #14271179 | 2 |
| C2×#11745173 | 2 |
| #14271136 | 2 |
| #14270924 | 2 |
| C29×#344 | 2 |
| #1906 | 29 |