Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
322 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 65 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. #14271125 | C2 | semidirect |
| 3. C22⋊C8×D29 | C2 | semidirect |
| 4. #14270887 | C2 | semidirect |
| 5. #14270886 | C2 | semidirect |
| 6. #14270886 | C2 | semidirect |
| 7. C29×#323 | C2 | semidirect |
| 137. #323 | D29 | semidirect |
| 166. C29 | #1471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745246 | 2 |
| #14271125 | 2 |
| C22⋊C8×D29 | 2 |
| #14270887 | 2 |
| #14270886 | 2 |
| C29×#323 | 2 |
| #1471 | 29 |