Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 149 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×#90773 | C2 | semidirect |
| 3. C2×#11745298 | C2 | semidirect |
| 4. C2×#11745255 | C2 | semidirect |
| 5. #14271377 | C2 | direct (N × H) |
| 6. C2×#11745162 | C2 | semidirect |
| 7. C2×#11745158 | C2 | semidirect |
| 8. C2×C29×#102 | C2 | semidirect |
| 18. #11745298 | C22 | semidirect |
| 25. C2×#90773 | C22 | semidirect |
| 27. #11745255 | C22 | semidirect |
| 28. C29×#102 | C22 | semidirect |
| 29. #11745162 | C22 | semidirect |
| 30. #11745158 | C22 | semidirect |
| 125. C2×#102 | D29 | semidirect |
| 127. C2×C29 | #463 | semidirect |
| 153. #102 | C2×D29 | semidirect |
| 154. C29 | C2×#463 | semidirect |
| 243. C2 | #14271377 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90773 | 2 |
| C22×#90782 | 2 |
| C2×#11745298 | 2 |
| C2×#11745255 | 2 |
| #14271377 | 2 |
| C2×#11745162 | 2 |
| C2×#11745158 | 2 |
| C2×C29×#102 | 2 |
| C2×#463 | 29 |