Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
162 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×#66876 | C2 | semidirect |
| 3. C22⋊(C11⋊C16) | C2 | semidirect |
| 4. C4⋊(C11⋊C16) | C2 | semidirect |
| 5. C4×C11⋊C16 | C2 | semidirect |
| 27. C11⋊C16 | D4 | semidirect |
| 52. C4×C11 | M32 | semidirect |
| 81. C11 | #2169 | semidirect |
| 100. C4 | #66876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×D4×C11 | 2 |
| C2×#66876 | 2 |
| C22⋊(C11⋊C16) | 2 |
| C4⋊(C11⋊C16) | 2 |
| C4×C11⋊C16 | 2 |
| #2169 | 11 |