Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#90784 | C2 | semidirect |
| 3. #14271737 | C2 | semidirect |
| 4. #14271324 | C2 | semidirect |
| 5. #14271312 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. #14271159 | C2 | semidirect |
| 8. #14271131 | C2 | semidirect |
| 9. C2×C29×#137 | C2 | semidirect |
| 11. C22×Q8×C29 | C22 | semidirect |
| 22. C2×Q16×C29 | C22 | semidirect |
| 23. C2×SD16×C29 | C22 | semidirect |
| 24. C2×M16×C29 | C22 | semidirect |
| 26. #11745308 | C22 | semidirect |
| 29. C2×#90784 | C22 | semidirect |
| 31. #11745288 | C22 | semidirect |
| 32. C22×#6597 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745180 | C22 | semidirect |
| 35. #11745169 | C22 | semidirect |
| 36. #11745168 | C22 | semidirect |
| 142. C2×#137 | D29 | semidirect |
| 162. C22×Q8 | C2×D29 | semidirect |
| 168. C2×Q16 | C2×D29 | semidirect |
| 171. C2×SD16 | C2×D29 | semidirect |
| 172. C2×M16 | C2×D29 | semidirect |
| 183. C29 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| C22×#90784 | 2 |
| #14271737 | 2 |
| #14271324 | 2 |
| #14271312 | 2 |
| #14271169 | 2 |
| #14271159 | 2 |
| #14271131 | 2 |
| C2×C29×#137 | 2 |
| #3009 | 29 |