Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#90784 | C2 | semidirect |
| 3. C2×C4×D116 | C2 | semidirect |
| 4. #14271375 | C2 | direct (N × H) |
| 5. C2×C4⋊#6597 | C2 | semidirect |
| 6. C2×#11745183 | C2 | semidirect |
| 7. C2×#11745180 | C2 | semidirect |
| 8. C2×C29×#124 | C2 | semidirect |
| 14. C29×#124 | C22 | semidirect |
| 19. C2×#90784 | C22 | semidirect |
| 27. C4×D116 | C22 | semidirect |
| 28. #11745183 | C22 | semidirect |
| 29. #11745180 | C22 | semidirect |
| 30. C4⋊#6597 | C22 | semidirect |
| 120. C2×#124 | D29 | semidirect |
| 127. C2×C29 | #463 | semidirect |
| 143. #124 | C2×D29 | semidirect |
| 154. C29 | C2×#463 | semidirect |
| 243. C2 | #14271375 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90784 | 2 |
| C22×#90782 | 2 |
| C2×C4×D116 | 2 |
| #14271375 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×#11745183 | 2 |
| C2×#11745180 | 2 |
| C2×C29×#124 | 2 |
| C2×#463 | 29 |