Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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×#135 | C2 | semidirect |
| 2. C2×#66892 | C2 | semidirect |
| 3. C2×#66890 | C2 | semidirect |
| 4. #10622728 | C2 | semidirect |
| 5. #10622202 | C2 | semidirect |
| 6. #10622200 | C2 | semidirect |
| 7. C22⋊(C11⋊C16) | C2 | semidirect |
| 33. C11×Q16 | D4 | semidirect |
| 36. C11×D8 | D4 | semidirect |
| 69. C2×#135 | D11 | semidirect |
| 122. Q16 | C22⋊D11 | semidirect |
| 127. D8 | C22⋊D11 | semidirect |
| 136. C11 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#135 | 2 |
| C2×#66892 | 2 |
| C2×#66890 | 2 |
| #10622728 | 2 |
| #10622202 | 2 |
| #10622200 | 2 |
| C22⋊(C11⋊C16) | 2 |
| #2186 | 11 |