Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×C22⋊#6597 | C2 | semidirect |
| 2. C4×C22⋊Dic29 | C2 | semidirect |
| 3. #14270900 | C2 | semidirect |
| 4. #14270897 | C2 | semidirect |
| 6. C2×#41×C29 | C4 | semidirect |
| 9. C29×C22⋊Q8 | C4 | semidirect |
| 11. C29×#121 | C4 | semidirect |
| 16. C29×#117 | C4 | semidirect |
| 118. C2×#41 | Dic29 | semidirect |
| 122. C22⋊Q8 | Dic29 | semidirect |
| 124. #121 | Dic29 | semidirect |
| 129. #117 | Dic29 | semidirect |
| 135. C29 | #1501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#6597 | 2 |
| C4×C22⋊Dic29 | 2 |
| #14270900 | 2 |
| #14270897 | 2 |
| C29×#525 | 2 |
| #1501 | 29 |