Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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 |
|---|---|---|
| 1. #13079178 | C2 | semidirect |
| 2. #13079177 | C2 | semidirect |
| 3. #13079125 | C2 | semidirect |
| 5. #13068247 | C2 | semidirect |
| 6. #13068245 | C2 | semidirect |
| 7. #13068244 | C2 | semidirect |
| 8. #13068241 | C2 | semidirect |
| 9. #13068240 | C2 | semidirect |
| 10. D11×#322 | C2 | semidirect |
| 11. C11×#1716 | C2 | semidirect |
| 131. C8×D11 | SD16 | semidirect |
| 137. #1716 | D11 | semidirect |
| 311. C11 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13079178 | 2 |
| #13079177 | 2 |
| #13079125 | 2 |
| #13079045 | 2 |
| #13068247 | 2 |
| #13068245 | 2 |
| #13068244 | 2 |
| #13068241 | 2 |
| #13068240 | 2 |
| D11×#322 | 2 |
| C11×#1716 | 2 |
| #19608 | 11 |