Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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. #10623001 | C2 | semidirect |
| 3. #10622838 | C2 | semidirect |
| 5. #10622669 | C2 | semidirect |
| 6. #10622668 | C2 | semidirect |
| 7. C4×#4318 | C2 | semidirect |
| 18. #66923 | C22 | semidirect |
| 19. #66922 | C22 | semidirect |
| 21. #66899 | C22 | semidirect |
| 23. #66867 | C22 | semidirect |
| 24. C4×C11⋊C8 | C22 | semidirect |
| 131. C11 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#124 | 2 |
| #10623001 | 2 |
| #10622838 | 2 |
| #10622828 | 2 |
| #10622669 | 2 |
| #10622668 | 2 |
| C4×#4318 | 2 |
| #3140 | 11 |