Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#90807 | C2 | semidirect |
| 3. #14271275 | C2 | semidirect |
| 4. #14271271 | C2 | semidirect |
| 5. #14271269 | C2 | semidirect |
| 6. #14271263 | C2 | semidirect |
| 7. #14271260 | C2 | semidirect |
| 8. #14271198 | C2 | semidirect |
| 9. #14271156 | C2 | semidirect |
| 10. #97×D29 | C2 | semidirect |
| 11. C29×#442 | C2 | semidirect |
| 19. #11745274 | C4 | semidirect |
| 46. #90807 | C2×C4 | semidirect |
| 50. D8×C29 | C2×C4 | semidirect |
| 57. #90783 | C2×C4 | semidirect |
| 69. Dic116 | C2×C4 | semidirect |
| 71. C8×D29 | C2×C4 | semidirect |
| 114. #442 | D29 | semidirect |
| 154. C29 | #2943 | semidirect |
| 167. D8 | C4×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745274 | 2 |
| C4×#90807 | 2 |
| #14271275 | 2 |
| #14271271 | 2 |
| #14271269 | 2 |
| #14271263 | 2 |
| #14271260 | 2 |
| #14271198 | 2 |
| #14271156 | 2 |
| #97×D29 | 2 |
| C29×#442 | 2 |
| #2943 | 29 |