Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
642 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 215 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. #13069336 | C2 | semidirect |
| 4. #13069177 | C2 | semidirect |
| 6. #13068759 | C2 | semidirect |
| 7. C11×#1842 | C2 | semidirect |
| 66. C42×C11 | M16 | semidirect |
| 82. #1842 | D11 | semidirect |
| 193. C42 | #4313 | semidirect |
| 194. C11 | #23378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#66929 | 2 |
| #13069336 | 2 |
| #13069228 | 2 |
| #13069177 | 2 |
| #13068797 | 2 |
| #13068759 | 2 |
| C11×#1842 | 2 |
| #23378 | 11 |