Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×#11745176 | C2 | semidirect |
| 3. #14271401 | C2 | semidirect |
| 4. #14270965 | C2 | semidirect |
| 5. #14270964 | C2 | semidirect |
| 6. #14270942 | C2 | semidirect |
| 7. C2×C29×SD32 | C2 | semidirect |
| 9. C2×Q16×C29 | C22 | semidirect |
| 18. C2×C16×C29 | C22 | semidirect |
| 21. #11745166 | C22 | semidirect |
| 22. C2×#90768 | C22 | semidirect |
| 80. C2×D29 | SD32 | semidirect |
| 88. C2×SD32 | D29 | semidirect |
| 100. C2×Q16 | C2×D29 | semidirect |
| 111. C2×C16 | C2×D29 | semidirect |
| 114. C29 | #2187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D29 | 2 |
| C2×#11745176 | 2 |
| #14271401 | 2 |
| #14270965 | 2 |
| #14270964 | 2 |
| #14270942 | 2 |
| C2×C29×SD32 | 2 |
| #2187 | 29 |