Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. C2×C4×D116 | C2 | semidirect |
| 3. C4×D232 | C2 | direct (N × H) |
| 4. C2×#11745166 | C2 | semidirect |
| 5. C2×#11745169 | C2 | semidirect |
| 6. C2×C4×C8×C29 | C2 | semidirect |
| 14. C2×D232 | C4 | direct (N × H) |
| 17. C4×D116 | C22 | semidirect |
| 18. C4×C8×C29 | C22 | semidirect |
| 19. #11745169 | C22 | semidirect |
| 20. #11745166 | C22 | semidirect |
| 28. C2×D116 | C2×C4 | semidirect |
| 33. C2×C8×C29 | C2×C4 | semidirect |
| 41. D232 | C2×C4 | direct (N × H) |
| 48. C2×C4×C29 | D8 | semidirect |
| 59. D116 | C22×C4 | semidirect |
| 62. C8×C29 | C22×C4 | semidirect |
| 74. C4×C29 | C2×D8 | semidirect |
| 83. C2×C4×C8 | D29 | semidirect |
| 84. C2×C29 | C4×D8 | semidirect |
| 102. C4×C8 | C2×D29 | semidirect |
| 103. C29 | C2×C4×D8 | semidirect |
| 117. C2×C8 | C4×D29 | semidirect |
| 137. C2×C4 | D232 | direct (N × H) |
| 145. C8 | C2×C4×D29 | semidirect |
| 157. C4 | C2×D232 | direct (N × H) |
| 161. C2 | C4×D232 | 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 |
| C2×C4×D116 | 2 |
| C4×D232 | 2 |
| C2×#11745166 | 2 |
| C2×#11745169 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×C4×D8 | 29 |