Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271737 | C2 | semidirect |
| 3. #14271352 | C2 | semidirect |
| 4. #14271137 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. C29×#536 | C2 | semidirect |
| 8. C22×Q8×C29 | C22 | semidirect |
| 19. C29×#123 | C22 | semidirect |
| 21. C29×#117 | C22 | semidirect |
| 25. #11745291 | C22 | semidirect |
| 26. #11745288 | C22 | semidirect |
| 27. #11745182 | C22 | semidirect |
| 28. #11745154 | C22 | semidirect |
| 126. #536 | D29 | semidirect |
| 144. C22×Q8 | C2×D29 | semidirect |
| 150. #123 | C2×D29 | semidirect |
| 154. #117 | C2×D29 | semidirect |
| 157. C29 | #3028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| #14271737 | 2 |
| #14271352 | 2 |
| #14271137 | 2 |
| #14271136 | 2 |
| C29×#536 | 2 |
| #3028 | 29 |