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. C2×#11745304 | C2 | semidirect |
| 3. #14271737 | C2 | semidirect |
| 4. #14271322 | C2 | semidirect |
| 5. #14271312 | C2 | semidirect |
| 6. #14271168 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. #14271129 | C2 | semidirect |
| 9. C22×SD16×C29 | C2 | semidirect |
| 10. C22×Q8×C29 | C22 | semidirect |
| 22. C2×SD16×C29 | C22 | semidirect |
| 23. C22×C8×C29 | C22 | semidirect |
| 25. #11745308 | C22 | semidirect |
| 27. C2×#90785 | C22 | semidirect |
| 29. C2×#90784 | C22 | semidirect |
| 31. #11745288 | C22 | semidirect |
| 32. C2×#90777 | C22 | semidirect |
| 33. #11745180 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 143. C22×SD16 | D29 | semidirect |
| 162. C22×Q8 | C2×D29 | semidirect |
| 171. C2×SD16 | C2×D29 | semidirect |
| 173. C22×C8 | 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×#11745359 | 2 |
| C2×#11745304 | 2 |
| #14271737 | 2 |
| #14271322 | 2 |
| #14271312 | 2 |
| #14271168 | 2 |
| #14271160 | 2 |
| #14271129 | 2 |
| C22×SD16×C29 | 2 |
| #3009 | 29 |