Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 482 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. C22×C11×Q16 | C2 | semidirect |
| 2. #10623348 | C2 | semidirect |
| 3. C2×#66972 | C2 | semidirect |
| 4. #10622840 | C2 | semidirect |
| 5. #10622804 | C2 | semidirect |
| 6. #10622801 | C2 | semidirect |
| 7. #10622800 | C2 | semidirect |
| 8. #10622798 | C2 | semidirect |
| 9. Q16×Dic11 | C2 | semidirect |
| 10. #10622728 | C2 | semidirect |
| 11. C8×C22⋊D11 | C2 | semidirect |
| 58. C11×Q16 | D4 | semidirect |
| 113. C22×Q16 | D11 | semidirect |
| 125. C22×C11 | #135 | semidirect |
| 194. Q16 | C22⋊D11 | semidirect |
| 216. C11 | #3285 | semidirect |
| 256. C22 | #66972 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×Q16 | 2 |
| #10623348 | 2 |
| C2×#66972 | 2 |
| #10622840 | 2 |
| #10622804 | 2 |
| #10622801 | 2 |
| #10622800 | 2 |
| #10622798 | 2 |
| Q16×Dic11 | 2 |
| #10622728 | 2 |
| C8×C22⋊D11 | 2 |
| #3285 | 11 |