Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #14271568 | C2 | semidirect |
| 4. #14271374 | C2 | semidirect |
| 5. #14270910 | C2 | semidirect |
| 6. #14270895 | C2 | semidirect |
| 52. D4×C29 | Q16 | semidirect |
| 117. C29 | #1649 | semidirect |
| 152. D4 | Dic116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic58 | 2 |
| #14271568 | 2 |
| #14271443 | 2 |
| #14271374 | 2 |
| #14270910 | 2 |
| #14270895 | 2 |
| C29×D4⋊C8 | 2 |
| #1649 | 29 |