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 |
|---|---|---|
| 1. C2×Q16×D11 | C2 | semidirect |
| 2. C22×Dic44 | C2 | semidirect |
| 4. C11×#467 | C2 | semidirect |
| 5. #10622794 | C2 | semidirect |
| 7. #10622663 | C2 | semidirect |
| 8. #10622500 | C2 | semidirect |
| 9. #10622486 | C2 | semidirect |
| 10. #10622421 | C2 | semidirect |
| 11. #10622406 | C2 | semidirect |
| 78. Dic44 | D4 | semidirect |
| 91. C22⋊D11 | Q16 | semidirect |
| 116. #467 | D11 | semidirect |
| 124. C22×C11 | C2×Q16 | semidirect |
| 128. C2×D11 | C2×Q16 | semidirect |
| 138. Dic11 | C2×Q16 | semidirect |
| 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 |
|---|---|
| C2×Q16×D11 | 2 |
| C22×Dic44 | 2 |
| #10623163 | 2 |
| C11×#467 | 2 |
| #10622794 | 2 |
| C8×C22⋊D11 | 2 |
| #10622663 | 2 |
| #10622500 | 2 |
| #10622486 | 2 |
| #10622421 | 2 |
| #10622406 | 2 |
| D4×Q16 | 11 |