Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×#90768 | C2 | semidirect |
| 3. #14270948 | C2 | direct (N × H) |
| 4. C2×C29×M32 | C2 | semidirect |
| 15. C29×M32 | C22 | semidirect |
| 19. C2×#90768 | C22 | semidirect |
| 79. C2×M32 | D29 | semidirect |
| 84. C2×C29 | #350 | semidirect |
| 97. M32 | C2×D29 | semidirect |
| 102. C29 | C2×#350 | semidirect |
| 163. C2 | #14270948 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745263 | 2 |
| C22×#90768 | 2 |
| #14270948 | 2 |
| C2×C29×M32 | 2 |
| C2×#350 | 29 |