Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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×C11×C22⋊Q8 | C2 | semidirect |
| 3. #10622844 | C2 | semidirect |
| 4. #10622825 | C2 | semidirect |
| 5. #10622607 | C2 | semidirect |
| 6. #10622605 | C2 | semidirect |
| 8. #10622559 | C2 | semidirect |
| 10. C22×Q8×C11 | C22 | semidirect |
| 14. C2×C11×C4⋊C4 | C22 | semidirect |
| 15. C2×C11×C4⋊C4 | C22 | semidirect |
| 23. C2×C4⋊Dic11 | C22 | semidirect |
| 24. C2×Dic11⋊C4 | C22 | semidirect |
| 25. C11⋊#95 | C22 | semidirect |
| 26. C11⋊#95 | C22 | semidirect |
| 32. C23×D11 | Q8 | semidirect |
| 89. C2×C22⋊Q8 | D11 | semidirect |
| 120. C22×Q8 | C2×D11 | semidirect |
| 126. C2×C4⋊C4 | C2×D11 | semidirect |
| 127. C2×C4⋊C4 | C2×D11 | semidirect |
| 173. C11 | #2626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×C22⋊Q8 | 2 |
| C22×(C2×D11)⋊C4 | 2 |
| #10622844 | 2 |
| #10622825 | 2 |
| #10622607 | 2 |
| #10622605 | 2 |
| #10622568 | 2 |
| #10622559 | 2 |
| #2626 | 11 |