Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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×#519 | C2 | semidirect |
| 2. C2×#66995 | C2 | semidirect |
| 3. C22×#4325 | C2 | semidirect |
| 5. #10622641 | C2 | semidirect |
| 6. #10622640 | C2 | semidirect |
| 7. #10622615 | C2 | semidirect |
| 8. #10622614 | C2 | semidirect |
| 9. #10622612 | C2 | semidirect |
| 14. C4×Q8×C11 | C22 | semidirect |
| 18. C2×#4326 | C22 | semidirect |
| 22. C2×#4325 | C22 | semidirect |
| 29. #66874 | C22 | semidirect |
| 31. #66873 | C22 | semidirect |
| 32. C4⋊(C11⋊C8) | C22 | semidirect |
| 36. C2×Q8×C11 | D4 | semidirect |
| 100. #519 | D11 | semidirect |
| 136. C4×Q8 | C2×D11 | semidirect |
| 155. C2×Q8 | D44 | semidirect |
| 183. C11 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#519 | 2 |
| C2×#66995 | 2 |
| C22×#4325 | 2 |
| #10623056 | 2 |
| #10622641 | 2 |
| #10622640 | 2 |
| #10622615 | 2 |
| #10622614 | 2 |
| #10622612 | 2 |
| #3043 | 11 |