Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #14271202 | C2 | direct (N × H) |
| 5. C2×#11745166 | C2 | semidirect |
| 6. C2×#11745155 | C2 | semidirect |
| 7. C2×#11745156 | C2 | semidirect |
| 8. C2×C29×#106 | C2 | semidirect |
| 20. C2×#90772 | C4 | semidirect |
| 26. C29×#106 | C22 | semidirect |
| 27. #11745166 | C22 | semidirect |
| 28. #11745156 | C22 | semidirect |
| 29. #11745155 | C22 | semidirect |
| 43. C2×C8×C29 | C2×C4 | semidirect |
| 56. C2×#6597 | C2×C4 | semidirect |
| 58. #90772 | C2×C4 | semidirect |
| 82. C8×C29 | C22×C4 | semidirect |
| 83. #6597 | C22×C4 | semidirect |
| 108. C2×#106 | D29 | semidirect |
| 109. C2×C29 | #428 | semidirect |
| 134. #106 | C2×D29 | semidirect |
| 135. C29 | C2×#428 | semidirect |
| 152. C2×C8 | C4×D29 | semidirect |
| 189. C8 | C2×C4×D29 | semidirect |
| 207. C2 | #14271202 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×#11745254 | 2 |
| C2×C4⋊C4×D29 | 2 |
| #14271202 | 2 |
| C2×#11745166 | 2 |
| C2×#11745155 | 2 |
| C2×#11745156 | 2 |
| C2×C29×#106 | 2 |
| C2×#428 | 29 |