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 |
| 2. C22×C8×D29 | C2 | semidirect |
| 3. C2×#11745308 | C2 | semidirect |
| 5. #14271395 | C2 | direct (N × H) |
| 6. C2×#11745156 | C2 | semidirect |
| 7. C2×#11745169 | C2 | semidirect |
| 8. C2×C29×#103 | C2 | semidirect |
| 16. #11745308 | C22 | semidirect |
| 18. C2×#90784 | C22 | semidirect |
| 25. C2×C8×D29 | C22 | semidirect |
| 28. C29×#103 | C22 | semidirect |
| 29. #11745169 | C22 | semidirect |
| 30. #11745156 | C22 | semidirect |
| 62. C2×#6597 | D4 | semidirect |
| 72. C22×D29 | SD16 | semidirect |
| 97. #6597 | C2×D4 | semidirect |
| 110. C2×D29 | C2×SD16 | semidirect |
| 124. C2×#103 | D29 | semidirect |
| 126. C2×C29 | #465 | semidirect |
| 152. #103 | C2×D29 | semidirect |
| 154. C29 | C2×#465 | semidirect |
| 243. C2 | #14271395 | 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×C8×D29 | 2 |
| C2×#11745308 | 2 |
| C2×#11745257 | 2 |
| #14271395 | 2 |
| C2×#11745156 | 2 |
| C2×#11745169 | 2 |
| C2×C29×#103 | 2 |
| C2×#465 | 29 |