Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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×#10622532 | C2 | semidirect |
| 2. C2×#10622525 | C2 | semidirect |
| 3. #13070924 | C2 | direct (N × H) |
| 4. C2×#10622160 | C2 | semidirect |
| 5. C2×#10622087 | C2 | semidirect |
| 6. C2×#10622157 | C2 | semidirect |
| 7. C2×D11×C32 | C2 | semidirect |
| 8. C2×C11×SD64 | C2 | semidirect |
| 16. #10622532 | C22 | semidirect |
| 18. #10622525 | C22 | semidirect |
| 22. C11×SD64 | C22 | semidirect |
| 24. #10622160 | C22 | semidirect |
| 25. #10622157 | C22 | semidirect |
| 27. #10622087 | C22 | semidirect |
| 28. D11×C32 | C22 | semidirect |
| 94. C2×SD64 | D11 | semidirect |
| 136. SD64 | C2×D11 | semidirect |
| 183. C2×C11 | #2262 | semidirect |
| 217. C11 | C2×#2262 | semidirect |
| 257. C2 | #13070924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622532 | 2 |
| C2×#10622525 | 2 |
| #13070924 | 2 |
| C2×#10622160 | 2 |
| C2×#10622087 | 2 |
| C2×#10622157 | 2 |
| C2×D11×C32 | 2 |
| C2×C11×SD64 | 2 |
| C2×#2262 | 11 |