Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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×#11745288 | C2 | semidirect |
| 3. #14271169 | C2 | direct (N × H) |
| 4. C2×#11745169 | C2 | semidirect |
| 5. C22×M16×C29 | C2 | semidirect |
| 11. C22×D116 | C4 | semidirect |
| 15. C2×M16×C29 | C22 | semidirect |
| 16. C22×C8×C29 | C22 | semidirect |
| 19. #11745288 | C22 | semidirect |
| 20. C2×C4⋊Dic29 | C22 | semidirect |
| 22. #11745169 | C22 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 46. C2×C8×C29 | C23 | semidirect |
| 49. C4⋊Dic29 | C23 | semidirect |
| 94. C22×M16 | D29 | semidirect |
| 99. C2×C29 | #418 | semidirect |
| 112. C2×M16 | C2×D29 | semidirect |
| 113. C22×C8 | C2×D29 | semidirect |
| 120. C29 | C2×#418 | semidirect |
| 144. C2×C8 | C22×D29 | semidirect |
| 192. C2 | #14271169 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C2×#11745288 | 2 |
| #14271169 | 2 |
| C2×#11745169 | 2 |
| C22×M16×C29 | 2 |
| C2×#418 | 29 |