Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C11×#550 | C2 | semidirect |
| 2. C2×#67003 | C2 | semidirect |
| 3. #10623084 | C2 | semidirect |
| 4. #10622851 | C2 | semidirect |
| 5. #10622688 | C2 | semidirect |
| 6. #10622686 | C2 | semidirect |
| 7. #10622651 | C2 | semidirect |
| 8. #10622650 | C2 | semidirect |
| 9. C4×#4326 | C2 | semidirect |
| 10. #10622640 | C2 | semidirect |
| 11. D4×C11⋊C8 | C2 | semidirect |
| 69. #4326 | D4 | semidirect |
| 120. #550 | D11 | semidirect |
| 143. C4×C11 | #135 | semidirect |
| 224. C11 | #3287 | semidirect |
| 276. C4 | #67003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#550 | 2 |
| C2×#67003 | 2 |
| #10623084 | 2 |
| #10622851 | 2 |
| #10622688 | 2 |
| #10622686 | 2 |
| #10622651 | 2 |
| #10622650 | 2 |
| C4×#4326 | 2 |
| #10622640 | 2 |
| D4×C11⋊C8 | 2 |
| #3287 | 11 |