Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×C11×Q16 | C2 | semidirect |
| 3. C2×Q16×D11 | C2 | semidirect |
| 4. #10622841 | C2 | semidirect |
| 5. #10622801 | C2 | semidirect |
| 6. #10622799 | C2 | semidirect |
| 7. Q16×Dic11 | C2 | semidirect |
| 8. #10622795 | C2 | semidirect |
| 9. #10622794 | C2 | semidirect |
| 10. #10622729 | C2 | semidirect |
| 57. C11×Q16 | D4 | semidirect |
| 95. C22⋊D11 | Q16 | direct (N × H) |
| 112. C22×Q16 | D11 | semidirect |
| 124. C22×C11 | C2×Q16 | semidirect |
| 128. C2×D11 | C2×Q16 | semidirect |
| 138. Dic11 | C2×Q16 | semidirect |
| 192. Q16 | C22⋊D11 | direct (N × H) |
| 212. C11 | D4×Q16 | semidirect |
| 248. C22 | Q16×D11 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×Q16 | 2 |
| Q8×C22⋊D11 | 2 |
| C2×Q16×D11 | 2 |
| #10622841 | 2 |
| #10622801 | 2 |
| #10622799 | 2 |
| Q16×Dic11 | 2 |
| #10622795 | 2 |
| #10622794 | 2 |
| #10622729 | 2 |
| C8×C22⋊D11 | 2 |
| D4×Q16 | 11 |