Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14271214 | C2 | semidirect |
| 3. C4⋊C8×D29 | C2 | semidirect |
| 4. #14270895 | C2 | semidirect |
| 5. #14270893 | C2 | semidirect |
| 6. D4⋊#6597 | C2 | semidirect |
| 7. C29×D4⋊C8 | C2 | semidirect |
| 33. #90807 | C8 | semidirect |
| 60. D4×C29 | C2×C8 | semidirect |
| 81. Dic58 | C2×C8 | semidirect |
| 111. D4⋊C8 | D29 | semidirect |
| 136. C29 | #1477 | semidirect |
| 173. D4 | C8×D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#90807 | 2 |
| #14271214 | 2 |
| C4⋊C8×D29 | 2 |
| #14270895 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| C29×D4⋊C8 | 2 |
| #1477 | 29 |