Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×C22⋊#6597 | C2 | semidirect |
| 3. #14270886 | C2 | direct (N × H) |
| 4. C2×C29×C22⋊C8 | C2 | semidirect |
| 17. C29×C22⋊C8 | C22 | semidirect |
| 19. C22⋊#6597 | C22 | semidirect |
| 26. C23×D29 | C8 | semidirect |
| 66. C22×D29 | C2×C8 | semidirect |
| 111. C2×C22⋊C8 | D29 | semidirect |
| 116. C2×C29 | #323 | semidirect |
| 135. C22⋊C8 | C2×D29 | semidirect |
| 136. C29 | C2×#323 | semidirect |
| 229. C2 | #14270886 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90781 | 2 |
| C2×C22⋊#6597 | 2 |
| #14270886 | 2 |
| C2×C29×C22⋊C8 | 2 |
| C2×#323 | 29 |