Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#11745232 | C2 | semidirect |
| 3. #14271532 | C2 | semidirect |
| 4. #14271528 | C2 | semidirect |
| 5. #14271518 | C2 | semidirect |
| 6. #14271165 | C2 | semidirect |
| 7. C4×M16×C29 | C2 | semidirect |
| 80. C4×M16 | D29 | semidirect |
| 102. C29 | #3142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| C2×#11745232 | 2 |
| #14271532 | 2 |
| #14271528 | 2 |
| #14271518 | 2 |
| #14271165 | 2 |
| C4×M16×C29 | 2 |
| #3142 | 29 |