Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#67004 | C2 | semidirect |
| 3. C2×#66954 | C2 | semidirect |
| 4. #10623057 | C2 | semidirect |
| 5. C11×#416 | C2 | semidirect |
| 6. C2×#66880 | C2 | semidirect |
| 7. #10622608 | C2 | semidirect |
| 8. #10622429 | C2 | semidirect |
| 9. #10622426 | C2 | semidirect |
| 10. #10622393 | C2 | semidirect |
| 11. #10622391 | C2 | semidirect |
| 81. #4318 | D4 | semidirect |
| 128. #416 | 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 |
|---|---|
| #10623364 | 2 |
| C2×#67004 | 2 |
| C2×#66954 | 2 |
| #10623057 | 2 |
| C11×#416 | 2 |
| C2×#66880 | 2 |
| #10622608 | 2 |
| #10622429 | 2 |
| #10622426 | 2 |
| #10622393 | 2 |
| #10622391 | 2 |
| #3063 | 11 |