Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C2×#11745304 | C2 | semidirect |
| 3. C2×#11745263 | C2 | semidirect |
| 4. #14271423 | C2 | direct (N × H) |
| 5. C2×#11745167 | C2 | semidirect |
| 6. C2×#11745184 | C2 | semidirect |
| 7. C2×#11745181 | C2 | semidirect |
| 8. C22×SD16×C29 | C2 | semidirect |
| 15. C2×SD16×C29 | C22 | semidirect |
| 19. #11745304 | C22 | semidirect |
| 29. #11745263 | C22 | semidirect |
| 32. #11745184 | C22 | semidirect |
| 33. #11745181 | C22 | semidirect |
| 34. #11745167 | C22 | semidirect |
| 135. C22×SD16 | D29 | semidirect |
| 144. C2×C29 | #471 | semidirect |
| 160. C2×SD16 | C2×D29 | semidirect |
| 173. C29 | C2×#471 | semidirect |
| 275. C2 | #14271423 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745304 | 2 |
| C2×#11745294 | 2 |
| C2×#11745263 | 2 |
| #14271423 | 2 |
| C2×#11745167 | 2 |
| C2×#11745184 | 2 |
| C2×#11745181 | 2 |
| C22×SD16×C29 | 2 |
| C2×#471 | 29 |