Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #14270990 | C2 | semidirect |
| 4. #14270967 | C2 | semidirect |
| 6. C4×#90768 | C2 | semidirect |
| 7. C4×Q16×C29 | C2 | semidirect |
| 15. #11745176 | C4 | direct (N × H) |
| 24. Q16×C29 | C2×C4 | semidirect |
| 36. #90768 | C2×C4 | semidirect |
| 60. C4×C29 | SD32 | semidirect |
| 65. C4×Q16 | D29 | semidirect |
| 87. C29 | C4×SD32 | semidirect |
| 92. Q16 | C4×D29 | semidirect |
| 128. C4 | #11745176 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745176 | 2 |
| C4×D232 | 2 |
| #14270990 | 2 |
| #14270967 | 2 |
| #14270963 | 2 |
| C4×#90768 | 2 |
| C4×Q16×C29 | 2 |
| C4×SD32 | 29 |