Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 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×Dic58 | C2 | semidirect |
| 4. C4×#90773 | C2 | direct (N × H) |
| 5. C2×#11745165 | C2 | semidirect |
| 6. C2×#11745164 | C2 | semidirect |
| 8. C2×C4×C8×C29 | C2 | semidirect |
| 20. C2×#90773 | C4 | direct (N × H) |
| 25. C4×Dic58 | C22 | semidirect |
| 26. C4×C8×C29 | C22 | semidirect |
| 28. #11745165 | C22 | semidirect |
| 29. #11745164 | C22 | semidirect |
| 45. C2×Dic58 | C2×C4 | semidirect |
| 48. C2×C8×C29 | C2×C4 | semidirect |
| 60. #90773 | C2×C4 | direct (N × H) |
| 67. C2×C4×C29 | SD16 | semidirect |
| 86. Dic58 | C22×C4 | semidirect |
| 88. C8×C29 | C22×C4 | semidirect |
| 100. C4×C29 | C2×SD16 | semidirect |
| 113. C2×C4×C8 | D29 | semidirect |
| 114. C2×C29 | C4×SD16 | semidirect |
| 139. C4×C8 | C2×D29 | semidirect |
| 140. C29 | C2×C4×SD16 | semidirect |
| 160. C2×C8 | C4×D29 | semidirect |
| 191. C2×C4 | #90773 | direct (N × H) |
| 199. C8 | C2×C4×D29 | semidirect |
| 213. C4 | C2×#90773 | direct (N × H) |
| 217. C2 | C4×#90773 | 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 |
| C2×C4×Dic58 | 2 |
| C2×C4×D116 | 2 |
| C4×#90773 | 2 |
| C2×#11745165 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×C4×SD16 | 29 |