Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #13068233 | C2 | semidirect |
| 5. #13066685 | C2 | semidirect |
| 6. #13066675 | C2 | semidirect |
| 7. C11×#1365 | C2 | semidirect |
| 64. D88 | Q16 | semidirect |
| 74. #1365 | D11 | semidirect |
| 170. C11 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13070764 | 2 |
| #13070760 | 2 |
| #13068233 | 2 |
| #13067410 | 2 |
| #13066685 | 2 |
| #13066675 | 2 |
| C11×#1365 | 2 |
| #12447 | 11 |