Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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. C2×#66886 | C2 | semidirect |
| 4. #10622732 | C2 | semidirect |
| 6. #10622577 | C2 | semidirect |
| 7. C11×#343 | C2 | semidirect |
| 81. #343 | D11 | semidirect |
| 147. C11 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10622744 | 2 |
| C2×#66887 | 2 |
| C2×#66886 | 2 |
| #10622732 | 2 |
| C2×#66873 | 2 |
| #10622577 | 2 |
| C11×#343 | 2 |
| #2063 | 11 |