Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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. #13077500 | C2 | semidirect |
| 3. C2×#10622156 | C2 | semidirect |
| 4. #13069512 | C2 | semidirect |
| 5. #13066721 | C2 | semidirect |
| 6. #13066701 | C2 | semidirect |
| 7. C11×#2145 | C2 | semidirect |
| 14. #10622808 | C4 | semidirect |
| 16. #10622806 | C4 | semidirect |
| 48. C2×Dic44 | C2×C4 | semidirect |
| 53. C2×D88 | C2×C4 | semidirect |
| 71. #66876 | C2×C4 | semidirect |
| 131. #2145 | D11 | semidirect |
| 317. C11 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13081750 | 2 |
| #13077500 | 2 |
| C2×#10622156 | 2 |
| #13069512 | 2 |
| #13066721 | 2 |
| #13066701 | 2 |
| C11×#2145 | 2 |
| #13030 | 11 |