Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1296 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 565 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×#66977 | C2 | semidirect |
| 4. #10623014 | C2 | direct (N × H) |
| 5. C2×#66931 | C2 | semidirect |
| 9. C22×Dic22 | C22 | semidirect |
| 15. C2×C4⋊Dic11 | C22 | semidirect |
| 16. #66977 | C22 | semidirect |
| 17. C2×Dic11⋊C4 | C22 | semidirect |
| 18. #66931 | C22 | semidirect |
| 20. C24×C11 | Q8 | semidirect |
| 31. C2×Dic22 | C23 | semidirect |
| 35. C4⋊Dic11 | C23 | semidirect |
| 36. Dic11⋊C4 | C23 | semidirect |
| 44. C23×C11 | C2×Q8 | semidirect |
| 87. C2×C11 | #543 | semidirect |
| 91. C24 | Dic22 | semidirect |
| 108. C11 | C2×#543 | semidirect |
| 115. C23 | C2×Dic22 | semidirect |
| 140. C2 | #10623014 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×C22⋊C4 | 2 |
| C22×C22⋊Dic11 | 2 |
| C2×#66977 | 2 |
| #10623014 | 2 |
| C2×#66931 | 2 |
| C2×#543 | 11 |