Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 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 |
|---|---|---|
| 1. #14271716 | C2 | semidirect |
| 5. #14270935 | C2 | semidirect |
| 6. #14270922 | C2 | semidirect |
| 7. C29×H(3,ℤ/4) | C2 | semidirect |
| 30. C2×D116 | Q8 | semidirect |
| 33. C2×Dic58 | Q8 | semidirect |
| 104. H(3,ℤ/4) | D29 | semidirect |
| 125. C29 | #2031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271716 | 2 |
| #14271181 | 2 |
| C2×#11745173 | 2 |
| #14271136 | 2 |
| #14270935 | 2 |
| #14270922 | 2 |
| C29×H(3,ℤ/4) | 2 |
| #2031 | 29 |