Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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⋊C8×D29 | C2 | semidirect |
| 3. #14270887 | C2 | semidirect |
| 4. #14270886 | C2 | semidirect |
| 5. C29×#323 | C2 | semidirect |
| 16. C29×C22⋊C8 | C22 | semidirect |
| 17. C22⋊#6597 | C22 | semidirect |
| 25. C23×D29 | C8 | semidirect |
| 49. C23×C29 | C2×C8 | semidirect |
| 68. C22×D29 | C2×C8 | semidirect |
| 118. #323 | D29 | direct (N × H) |
| 127. D29 | #323 | direct (N × H) |
| 140. C22⋊C8 | C2×D29 | semidirect |
| 141. C29 | C2×#323 | semidirect |
| 191. C23 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C4×D29 | 2 |
| C22⋊C8×D29 | 2 |
| #14270887 | 2 |
| #14270886 | 2 |
| C29×#323 | 2 |
| C2×#323 | 29 |