Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1434 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 275 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 |
|---|---|---|
| 2. #13069792 | C2 | direct (N × H) |
| 3. C2×#10622165 | C2 | semidirect |
| 4. C2×C11×#543 | C2 | semidirect |
| 7. C11×#543 | C22 | semidirect |
| 14. #10622165 | C22 | semidirect |
| 16. C24×D11 | Q8 | semidirect |
| 23. C22×C22⋊D11 | Q8 | semidirect |
| 26. C23×Dic11 | Q8 | semidirect |
| 55. C23×D11 | C2×Q8 | semidirect |
| 78. C22×Dic11 | C2×Q8 | semidirect |
| 88. C2×#543 | D11 | semidirect |
| 136. #543 | C2×D11 | semidirect |
| 205. C2×C11 | #2032 | semidirect |
| 252. C11 | C2×#2032 | semidirect |
| 329. C2 | #13069792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#66870 | 2 |
| #13069792 | 2 |
| C2×#10622165 | 2 |
| C2×C11×#543 | 2 |
| C2×#2032 | 11 |