Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×C4⋊Q8 | C2 | semidirect |
| 2. C22×#4326 | C2 | semidirect |
| 5. #10622699 | C2 | direct (N × H) |
| 6. C2×#66867 | C2 | semidirect |
| 11. C11×C4⋊Q8 | C22 | semidirect |
| 15. C2×#4326 | C22 | semidirect |
| 22. #66867 | C22 | semidirect |
| 70. C2×C4⋊Q8 | D11 | semidirect |
| 94. C4⋊Q8 | C2×D11 | semidirect |
| 101. C2×C11 | #497 | semidirect |
| 128. C11 | C2×#497 | semidirect |
| 162. C2 | #10622699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×C4⋊Q8 | 2 |
| C22×#4326 | 2 |
| C22×#4325 | 2 |
| C2×#66928 | 2 |
| #10622699 | 2 |
| C2×#66867 | 2 |
| C2×#497 | 11 |