Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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. Q8×Dic22 | C2 | semidirect |
| 3. C4×C11×Q16 | C2 | semidirect |
| 4. #10622798 | C2 | semidirect |
| 6. #10622634 | C2 | semidirect |
| 7. #10622503 | C2 | semidirect |
| 8. #10622430 | C2 | semidirect |
| 9. #10622408 | C2 | semidirect |
| 11. #10622292 | C2 | semidirect |
| 110. C4×Q16 | D11 | semidirect |
| 191. C11 | #3375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10623116 | 2 |
| Q8×Dic22 | 2 |
| C4×C11×Q16 | 2 |
| #10622798 | 2 |
| #10622640 | 2 |
| #10622634 | 2 |
| #10622503 | 2 |
| #10622430 | 2 |
| #10622408 | 2 |
| #10622307 | 2 |
| #10622292 | 2 |
| #3375 | 11 |