Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
342 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 121 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×D11×C32 | C2 | semidirect |
| 3. C22⋊(C11⋊C32) | C2 | semidirect |
| 4. (C2×D11)⋊C32 | C2 | semidirect |
| 5. C11×C22⋊C32 | C2 | semidirect |
| 14. C2×C11×C32 | C22 | semidirect |
| 15. C2×C11⋊C32 | C22 | semidirect |
| 69. C22⋊C32 | D11 | direct (N × H) |
| 73. C22×D11 | C32 | semidirect |
| 104. C2×C32 | C2×D11 | semidirect |
| 107. C22×C11 | C2×C32 | semidirect |
| 114. C2×D11 | C2×C32 | semidirect |
| 147. D11 | C22⋊C32 | direct (N × H) |
| 174. C11 | C2×C22⋊C32 | semidirect |
| 208. C22 | D11×C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D11 | 2 |
| C2×D11×C32 | 2 |
| C22⋊(C11⋊C32) | 2 |
| (C2×D11)⋊C32 | 2 |
| C11×C22⋊C32 | 2 |
| C2×C22⋊C32 | 11 |