Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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×D11×D16 | C2 | semidirect |
| 2. D11×#493 | C2 | semidirect |
| 3. #13070866 | C2 | semidirect |
| 4. #13070865 | C2 | semidirect |
| 5. #13070864 | C2 | semidirect |
| 6. C4×C16×D11 | C2 | semidirect |
| 7. C11×#2246 | C2 | semidirect |
| 11. C2×C11×D16 | C22 | semidirect |
| 12. C11×#493 | C22 | semidirect |
| 14. #10622764 | C22 | semidirect |
| 15. C2×#66890 | C22 | semidirect |
| 18. C2×D176 | C22 | semidirect |
| 20. #10622308 | C22 | semidirect |
| 22. C4×C11×C16 | C22 | semidirect |
| 23. C16×Dic11 | C22 | semidirect |
| 24. C4×C11⋊C16 | C22 | semidirect |
| 51. C16×D11 | D4 | semidirect |
| 80. C11×C16 | C2×D4 | semidirect |
| 81. C11⋊C16 | C2×D4 | semidirect |
| 87. #2246 | D11 | direct (N × H) |
| 106. C4×D11 | D16 | semidirect |
| 119. C2×D16 | C2×D11 | semidirect |
| 125. #493 | C2×D11 | semidirect |
| 129. C4×C16 | C2×D11 | semidirect |
| 138. C4×C11 | C2×D16 | semidirect |
| 142. Dic11 | C2×D16 | semidirect |
| 174. D11 | #2246 | direct (N × H) |
| 203. C16 | D4×D11 | semidirect |
| 204. C11 | C2×#2246 | semidirect |
| 239. C4 | D11×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D11×D16 | 2 |
| D11×#493 | 2 |
| #13070866 | 2 |
| #13070865 | 2 |
| #13070864 | 2 |
| C4×C16×D11 | 2 |
| C11×#2246 | 2 |
| C2×#2246 | 11 |