Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
6374 conjugacy classes of subgroups; only the 3275 normal subgroups are shown.
This group has 6374 conjugacy classes of subgroups — too many to draw. Only its 3275 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⋊#564 | C2 | semidirect |
| 2. D11×#564 | C2 | direct (N × H) |
| 4. C2×C11×#564 | C2 | semidirect |
| 5. C11×#564 | C22 | semidirect |
| 8. C11⋊#564 | C22 | semidirect |
| 39. C2×#564 | D11 | direct (N × H) |
| 50. #564 | C2×D11 | direct (N × H) |
| 60. C2×D11 | #564 | direct (N × H) |
| 76. C2×C11 | C2×#564 | semidirect |
| 78. D11 | C2×#564 | direct (N × H) |
| 89. C11 | C22×#564 | semidirect |
| 105. C2 | D11×#564 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11⋊#564 | 2 |
| D11×#564 | 2 |
| C2×D11×#125 | 2 |
| C2×C11×#564 | 2 |
| C22×#564 | 11 |