Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
214 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 57 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. #14271542 | C2 | semidirect |
| 3. #14271455 | C2 | semidirect |
| 4. #14270911 | C2 | semidirect |
| 5. #14270893 | C2 | semidirect |
| 51. D4×C29 | Q16 | semidirect |
| 112. C29 | #1632 | semidirect |
| 142. D4 | #90785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271870 | 2 |
| #14271542 | 2 |
| #14271455 | 2 |
| #14270911 | 2 |
| #14270893 | 2 |
| D4⋊#6597 | 2 |
| C29×#476 | 2 |
| #1632 | 29 |