Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
812 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 151 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. #13080291 | C2 | semidirect |
| 3. #13070699 | C2 | semidirect |
| 4. #13070648 | C2 | semidirect |
| 5. #13070526 | C2 | semidirect |
| 6. C4×D176 | C2 | semidirect |
| 7. C16×D44 | C2 | semidirect |
| 8. C11×#2246 | C2 | semidirect |
| 9. C2×D8×D11 | C22 | semidirect |
| 11. C2×C11×D16 | C22 | semidirect |
| 12. C2×C11×D16 | C22 | semidirect |
| 13. C11×#493 | C22 | semidirect |
| 14. #10622770 | C22 | semidirect |
| 16. C2×#66890 | C22 | semidirect |
| 20. C2×C16×D11 | C22 | semidirect |
| 21. C4×D88 | C22 | semidirect |
| 23. C4×C11×C16 | C22 | semidirect |
| 24. #10622200 | C22 | semidirect |
| 25. #10622147 | C22 | semidirect |
| 26. (C2×D11)⋊C16 | C22 | semidirect |
| 27. #10622142 | C22 | semidirect |
| 28. C4⋊(C11⋊C16) | C22 | semidirect |
| 56. D176 | D4 | semidirect |
| 86. D88 | C2×D4 | semidirect |
| 90. C11×C16 | C2×D4 | semidirect |
| 94. #2246 | D11 | semidirect |
| 119. D44 | D16 | semidirect |
| 132. C2×D16 | C2×D11 | semidirect |
| 133. C2×D16 | C2×D11 | semidirect |
| 135. #493 | C2×D11 | semidirect |
| 146. C4×C16 | C2×D11 | semidirect |
| 157. C2×D11 | C2×D16 | semidirect |
| 159. C4×C11 | C2×D16 | semidirect |
| 231. C16 | D4×D11 | semidirect |
| 232. C11 | D4×D16 | semidirect |
| 274. 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 |
| #13080291 | 2 |
| #13070699 | 2 |
| #13070648 | 2 |
| #13070526 | 2 |
| C4×D176 | 2 |
| C16×D44 | 2 |
| C11×#2246 | 2 |
| D4×D16 | 11 |