Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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. D11×Q64 | C2 | semidirect |
| 3. #13066833 | C2 | semidirect |
| 4. #13066832 | C2 | semidirect |
| 5. #13066830 | C2 | semidirect |
| 6. #13066826 | C2 | semidirect |
| 7. C11×Q128 | C2 | semidirect |
| 45. Q128 | D11 | semidirect |
| 103. C11 | #13743 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070926 | 2 |
| D11×Q64 | 2 |
| #13066833 | 2 |
| #13066832 | 2 |
| #13066830 | 2 |
| #13066826 | 2 |
| C11×Q128 | 2 |
| #13743 | 11 |