Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#11745270 | C2 | semidirect |
| 2. C2×#11745236 | C2 | semidirect |
| 3. C4×#90805 | C2 | semidirect |
| 4. #14271364 | C2 | semidirect |
| 5. #14271359 | C2 | semidirect |
| 6. #14271169 | C2 | semidirect |
| 7. C29×#423 | C2 | semidirect |
| 16. C2×D232 | C22 | semidirect |
| 17. C2×#90773 | C22 | semidirect |
| 21. C4×D116 | C22 | semidirect |
| 24. C4×Dic58 | C22 | semidirect |
| 25. C29×C4⋊C8 | C22 | semidirect |
| 26. #11745169 | C22 | semidirect |
| 32. #90805 | D4 | semidirect |
| 78. D116 | C2×D4 | semidirect |
| 82. Dic58 | C2×D4 | semidirect |
| 95. C4×C29 | AGL(1,ℤ/8) | semidirect |
| 105. #423 | D29 | semidirect |
| 129. C4⋊C8 | C2×D29 | semidirect |
| 131. C29 | #3038 | semidirect |
| 201. C4 | #11745270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745270 | 2 |
| C2×#11745236 | 2 |
| C4×#90805 | 2 |
| #14271364 | 2 |
| #14271359 | 2 |
| #14271169 | 2 |
| C29×#423 | 2 |
| #3038 | 29 |