Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1144 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 3. #14271025 | C2 | direct (N × H) |
| 4. C2×#11745179 | C2 | semidirect |
| 5. C2×#11745179 | C2 | semidirect |
| 6. C2×C29×#95 | C2 | semidirect |
| 13. C22×C4×D29 | C4 | semidirect |
| 17. C29×#95 | C22 | semidirect |
| 18. #11745179 | C22 | semidirect |
| 19. #11745179 | C22 | semidirect |
| 43. C2×C4×D29 | C2×C4 | semidirect |
| 102. C2×#95 | D29 | semidirect |
| 103. C2×C29 | #381 | semidirect |
| 122. #95 | C2×D29 | semidirect |
| 123. C29 | C2×#381 | semidirect |
| 201. C2 | #14271025 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D29 | 2 |
| C22×#90781 | 2 |
| #14271025 | 2 |
| C2×#11745179 | 2 |
| C2×C29×#95 | 2 |
| C2×#381 | 29 |