Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
166 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. #14272027 | C2 | semidirect |
| 4. #14272026 | C2 | semidirect |
| 5. #14272025 | C2 | semidirect |
| 6. #14272024 | C2 | semidirect |
| 58. C8×C29 | M16 | semidirect |
| 60. #6597 | M16 | semidirect |
| 100. C29 | #1569 | semidirect |
| 138. C8 | #90800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272184 | 2 |
| #14272166 | 2 |
| #14272027 | 2 |
| #14272026 | 2 |
| #14272025 | 2 |
| #14272024 | 2 |
| M16×Dic29 | 2 |
| #1569 | 29 |