Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#90809 | C2 | semidirect |
| 2. C22×#90784 | C2 | semidirect |
| 3. C22×D232 | C2 | semidirect |
| 4. C2×#11745257 | C2 | semidirect |
| 5. #14271311 | C2 | direct (N × H) |
| 6. C2×#11745157 | C2 | semidirect |
| 7. C2×#11745168 | C2 | semidirect |
| 8. C2×C29×#103 | C2 | semidirect |
| 13. C2×#90809 | C22 | semidirect |
| 23. C2×#90784 | C22 | semidirect |
| 27. C2×D232 | C22 | semidirect |
| 29. #11745257 | C22 | semidirect |
| 30. C29×#103 | C22 | semidirect |
| 31. #11745168 | C22 | semidirect |
| 32. #11745157 | C22 | semidirect |
| 38. C2×Q8×C29 | D4 | semidirect |
| 56. C2×D116 | D4 | semidirect |
| 89. Q8×C29 | C2×D4 | semidirect |
| 107. D116 | C2×D4 | semidirect |
| 142. C2×#103 | D29 | semidirect |
| 145. C2×C29 | #449 | semidirect |
| 173. #103 | C2×D29 | semidirect |
| 176. C29 | C2×#449 | semidirect |
| 185. C2×Q8 | D116 | semidirect |
| 233. Q8 | C2×D116 | semidirect |
| 283. C2 | #14271311 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90809 | 2 |
| C22×#90784 | 2 |
| C22×D232 | 2 |
| C2×#11745257 | 2 |
| #14271311 | 2 |
| C2×#11745157 | 2 |
| C2×#11745168 | 2 |
| C2×C29×#103 | 2 |
| C2×#449 | 29 |