Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
324 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 71 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. #13070889 | C2 | semidirect |
| 3. #13070750 | C2 | semidirect |
| 4. #13066672 | C2 | semidirect |
| 5. #13066576 | C2 | semidirect |
| 6. D4⋊(C11⋊C16) | C2 | semidirect |
| 7. C11×#1673 | C2 | semidirect |
| 88. #1673 | D11 | semidirect |
| 217. C11 | #12392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13080964 | 2 |
| #13070889 | 2 |
| #13070750 | 2 |
| #13066672 | 2 |
| #13066576 | 2 |
| D4⋊(C11⋊C16) | 2 |
| C11×#1673 | 2 |
| #12392 | 11 |