Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C11×#131 | C2 | semidirect |
| 3. #10623356 | C2 | semidirect |
| 4. C2×#66962 | C2 | semidirect |
| 5. #10622750 | C2 | semidirect |
| 6. #10622747 | C2 | semidirect |
| 7. #10622734 | C2 | semidirect |
| 8. #10622729 | C2 | semidirect |
| 9. #10622727 | C2 | semidirect |
| 10. #10622726 | C2 | semidirect |
| 11. C2×#66880 | C2 | semidirect |
| 64. C11×M16 | D4 | semidirect |
| 120. C2×#131 | D11 | semidirect |
| 209. M16 | C22⋊D11 | semidirect |
| 228. C11 | #3063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#131 | 2 |
| #10623364 | 2 |
| #10623356 | 2 |
| C2×#66962 | 2 |
| #10622750 | 2 |
| #10622747 | 2 |
| #10622734 | 2 |
| #10622729 | 2 |
| #10622727 | 2 |
| #10622726 | 2 |
| C2×#66880 | 2 |
| #3063 | 11 |