Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
182 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 63 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. #14271242 | C2 | semidirect |
| 3. C8×D116 | C2 | semidirect |
| 4. #14270914 | C2 | semidirect |
| 5. #14270892 | C2 | semidirect |
| 6. #14270892 | C2 | semidirect |
| 7. C29×#322 | C2 | semidirect |
| 52. D116 | M16 | semidirect |
| 85. #322 | D29 | semidirect |
| 106. C29 | #1586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D232 | 2 |
| #14271242 | 2 |
| C8×D116 | 2 |
| #14270914 | 2 |
| #14270892 | 2 |
| C29×#322 | 2 |
| #1586 | 29 |