Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 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×D232 | C2 | semidirect |
| 2. C22×#90782 | C2 | semidirect |
| 3. C2×#11745302 | C2 | semidirect |
| 4. C2×#11745255 | C2 | semidirect |
| 5. #14271357 | C2 | direct (N × H) |
| 6. C2×#11745162 | C2 | semidirect |
| 7. C2×#11745157 | C2 | semidirect |
| 8. C2×C29×#102 | C2 | semidirect |
| 18. #11745302 | C22 | semidirect |
| 20. C2×#90782 | C22 | semidirect |
| 25. C2×D232 | C22 | semidirect |
| 27. #11745255 | C22 | semidirect |
| 28. C29×#102 | C22 | semidirect |
| 29. #11745162 | C22 | semidirect |
| 30. #11745157 | C22 | semidirect |
| 51. C2×D116 | D4 | semidirect |
| 92. C2×Dic29 | D8 | semidirect |
| 100. D116 | C2×D4 | semidirect |
| 126. Dic29 | C2×D8 | semidirect |
| 134. C2×#102 | D29 | semidirect |
| 136. C2×C29 | #459 | semidirect |
| 163. #102 | C2×D29 | semidirect |
| 164. C29 | C2×#459 | semidirect |
| 263. C2 | #14271357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| C22×#90782 | 2 |
| C2×#11745302 | 2 |
| C2×#11745255 | 2 |
| #14271357 | 2 |
| C2×#11745162 | 2 |
| C2×#11745157 | 2 |
| C2×C29×#102 | 2 |
| C2×#459 | 29 |