Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. M32×D29 | C2 | semidirect |
| 3. C2×C16×D29 | C2 | semidirect |
| 4. #14270948 | C2 | semidirect |
| 5. #14270947 | C2 | semidirect |
| 6. #14270946 | C2 | semidirect |
| 7. C29×#350 | C2 | semidirect |
| 19. C29×M32 | C22 | semidirect |
| 20. C2×C16×C29 | C22 | semidirect |
| 21. #11745160 | C22 | semidirect |
| 22. C2×#90768 | C22 | semidirect |
| 109. #350 | D29 | direct (N × H) |
| 115. D29 | #350 | direct (N × H) |
| 129. M32 | C2×D29 | semidirect |
| 134. C2×C16 | C2×D29 | semidirect |
| 135. C29 | C2×#350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D29 | 2 |
| M32×D29 | 2 |
| C2×C16×D29 | 2 |
| #14270948 | 2 |
| #14270947 | 2 |
| #14270946 | 2 |
| C29×#350 | 2 |
| C2×#350 | 29 |