Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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. #14271198 | C2 | direct (N × H) |
| 4. C2×#11745155 | C2 | semidirect |
| 5. C2×#11745165 | C2 | semidirect |
| 6. C2×C29×#106 | C2 | semidirect |
| 14. C2×C8×D29 | C4 | semidirect |
| 18. C29×#106 | C22 | semidirect |
| 19. #11745165 | C22 | semidirect |
| 20. #11745155 | C22 | semidirect |
| 40. C8×D29 | C2×C4 | semidirect |
| 78. C2×#106 | D29 | semidirect |
| 79. C2×C29 | #427 | semidirect |
| 96. #106 | C2×D29 | semidirect |
| 97. C29 | C2×#427 | semidirect |
| 150. C2 | #14271198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×#11745254 | 2 |
| #14271198 | 2 |
| C2×#11745155 | 2 |
| C2×#11745165 | 2 |
| C2×C29×#106 | 2 |
| C2×#427 | 29 |