Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 324 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. #14271929 | C2 | semidirect |
| 3. #14271181 | C2 | semidirect |
| 4. #14271167 | C2 | semidirect |
| 5. C2×#11745171 | C2 | semidirect |
| 6. #14270921 | C2 | semidirect |
| 7. C29×#344 | C2 | semidirect |
| 19. C2×D232 | C4 | semidirect |
| 20. C2×#90773 | C4 | semidirect |
| 112. #344 | D29 | semidirect |
| 137. C29 | #1903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| #14271929 | 2 |
| #14271181 | 2 |
| #14271167 | 2 |
| C2×#11745171 | 2 |
| #14270921 | 2 |
| C29×#344 | 2 |
| #1903 | 29 |