Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#90805 | C2 | semidirect |
| 3. C4×Dic116 | C2 | semidirect |
| 4. C4×#90773 | C2 | semidirect |
| 5. C4×D232 | C2 | semidirect |
| 6. #14271201 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. C2×C4×C8×C29 | C2 | semidirect |
| 16. #11745266 | C4 | direct (N × H) |
| 33. #90805 | C2×C4 | semidirect |
| 39. C2×C8×C29 | C2×C4 | semidirect |
| 52. Dic116 | C2×C4 | semidirect |
| 53. D232 | C2×C4 | semidirect |
| 54. #90773 | C2×C4 | semidirect |
| 84. C4×C29 | #135 | semidirect |
| 96. C2×C4×C8 | D29 | semidirect |
| 121. C29 | C4×#135 | semidirect |
| 135. C2×C8 | C4×D29 | semidirect |
| 178. C4 | #11745266 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C4×#90805 | 2 |
| C4×Dic116 | 2 |
| C4×#90773 | 2 |
| C4×D232 | 2 |
| #14271201 | 2 |
| #14271160 | 2 |
| C2×C4×C8×C29 | 2 |
| C4×#135 | 29 |