Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
33214 conjugacy classes of subgroups; only the 3307 normal subgroups are shown.
This group has 33214 conjugacy classes of subgroups — too many to draw. Only its 3307 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. C23×C22⋊Dic11 | C2 | semidirect |
| 2. C2×#10622860 | C2 | direct (N × H) |
| 5. C26×C11 | C4 | semidirect |
| 8. C24×Dic11 | C22 | semidirect |
| 10. C22×C22⋊Dic11 | C22 | semidirect |
| 11. #10622860 | C22 | direct (N × H) |
| 17. C25×C11 | C2×C4 | semidirect |
| 23. C23×Dic11 | C23 | semidirect |
| 25. C2×C22⋊Dic11 | C23 | semidirect |
| 34. C24×C11 | C22⋊C4 | semidirect |
| 37. C24×C11 | C22×C4 | semidirect |
| 44. C22×Dic11 | C24 | semidirect |
| 57. C23×C11 | C2×C22⋊C4 | semidirect |
| 67. C26 | Dic11 | semidirect |
| 78. C22×C11 | #379 | semidirect |
| 80. C22×C11 | C22×C22⋊C4 | semidirect |
| 90. C25 | C2×Dic11 | semidirect |
| 100. C2×C11 | C2×#379 | semidirect |
| 110. C24 | C22⋊Dic11 | semidirect |
| 113. C24 | C22×Dic11 | semidirect |
| 122. C11 | C22×#379 | semidirect |
| 131. C23 | C2×C22⋊Dic11 | semidirect |
| 144. C22 | #10622860 | direct (N × H) |
| 146. C22 | C22×C22⋊Dic11 | semidirect |
| 152. C2 | C2×#10622860 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊Dic11 | 2 |
| C2×#10622860 | 2 |
| C27×C11 | 2 |
| C22×#379 | 11 |