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×#90782 | C2 | direct (N × H) |
| 4. C2×#11745155 | C2 | semidirect |
| 5. C2×#11745180 | C2 | semidirect |
| 6. C2×#11745157 | C2 | semidirect |
| 7. C2×C4×#6597 | C2 | semidirect |
| 8. C2×C4×D4×C29 | C2 | semidirect |
| 14. C4×D4×C29 | C22 | semidirect |
| 18. C2×#90782 | C4 | direct (N × H) |
| 25. C4×D116 | C22 | semidirect |
| 26. #11745180 | C22 | semidirect |
| 27. #11745157 | C22 | semidirect |
| 28. #11745155 | C22 | semidirect |
| 29. C4×#6597 | C22 | semidirect |
| 34. C2×D4×C29 | C2×C4 | semidirect |
| 45. C2×D116 | C2×C4 | semidirect |
| 54. #90782 | C2×C4 | direct (N × H) |
| 59. C2×#6597 | C2×C4 | semidirect |
| 73. D4×C29 | C22×C4 | semidirect |
| 78. C2×C4×C29 | D8 | semidirect |
| 89. D116 | C22×C4 | semidirect |
| 92. #6597 | C22×C4 | semidirect |
| 109. C4×C29 | C2×D8 | semidirect |
| 115. C2×C4×D4 | D29 | semidirect |
| 122. C2×C29 | C4×D8 | semidirect |
| 138. C4×D4 | C2×D29 | semidirect |
| 148. C29 | C2×C4×D8 | semidirect |
| 157. C2×D4 | C4×D29 | semidirect |
| 195. D4 | C2×C4×D29 | semidirect |
| 203. C2×C4 | #90782 | direct (N × H) |
| 228. C4 | C2×#90782 | direct (N × H) |
| 233. C2 | C4×#90782 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90782 | 2 |
| C2×C4×D116 | 2 |
| C4×#90782 | 2 |
| C2×#11745155 | 2 |
| C2×#11745180 | 2 |
| C2×#11745157 | 2 |
| C2×C4×#6597 | 2 |
| C2×C4×D4×C29 | 2 |
| C2×C4×D8 | 29 |