Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
774 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 255 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×#11745310 | C2 | semidirect |
| 3. #14271131 | C2 | semidirect |
| 4. #14271129 | C2 | semidirect |
| 5. #14271126 | C2 | semidirect |
| 6. C2×#11745168 | C2 | semidirect |
| 7. C2×C29×#131 | C2 | semidirect |
| 18. C2×M16×C29 | C22 | semidirect |
| 19. C22×C8×C29 | C22 | semidirect |
| 21. C2×#90777 | C22 | semidirect |
| 22. C22×#6597 | C22 | semidirect |
| 25. #11745168 | C22 | semidirect |
| 26. #11745168 | C22 | semidirect |
| 27. #11745168 | C22 | semidirect |
| 97. C2×D29 | #131 | semidirect |
| 105. C2×#131 | D29 | semidirect |
| 128. C2×M16 | C2×D29 | semidirect |
| 130. C22×C8 | C2×D29 | semidirect |
| 136. C29 | #2880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×D29 | 2 |
| C2×#11745310 | 2 |
| #14271131 | 2 |
| #14271129 | 2 |
| #14271126 | 2 |
| C2×#11745168 | 2 |
| C2×C29×#131 | 2 |
| #2880 | 29 |