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 |
|---|---|---|
| 3. C4×#90784 | C2 | direct (N × H) |
| 4. C2×#11745156 | C2 | semidirect |
| 5. C2×#11745183 | C2 | semidirect |
| 7. C2×C4×#6597 | C2 | semidirect |
| 8. C2×C4×Q8×C29 | C2 | semidirect |
| 13. C4×Q8×C29 | C22 | semidirect |
| 18. C2×#90784 | C4 | direct (N × H) |
| 26. #11745183 | C22 | semidirect |
| 28. #11745156 | C22 | semidirect |
| 29. C4×#6597 | C22 | semidirect |
| 33. C2×Q8×C29 | C2×C4 | semidirect |
| 53. #90784 | C2×C4 | direct (N × H) |
| 58. C2×#6597 | C2×C4 | semidirect |
| 68. Q8×C29 | C22×C4 | semidirect |
| 74. C2×C4×C29 | SD16 | semidirect |
| 88. #6597 | C22×C4 | semidirect |
| 102. C4×C29 | C2×SD16 | semidirect |
| 107. C2×C4×Q8 | D29 | semidirect |
| 114. C2×C29 | C4×SD16 | semidirect |
| 127. C4×Q8 | C2×D29 | semidirect |
| 140. C29 | C2×C4×SD16 | semidirect |
| 144. C2×Q8 | C4×D29 | semidirect |
| 179. Q8 | C2×C4×D29 | semidirect |
| 191. C2×C4 | #90784 | direct (N × H) |
| 213. C4 | C2×#90784 | direct (N × H) |
| 217. C2 | C4×#90784 | 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 |
| C2×C4×D116 | 2 |
| C4×#90784 | 2 |
| C2×#11745156 | 2 |
| C2×#11745183 | 2 |
| C2×#11745157 | 2 |
| C2×C4×#6597 | 2 |
| C2×C4×Q8×C29 | 2 |
| C2×C4×SD16 | 29 |