Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
380 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 380 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. C2×#10622131 | C2 | semidirect |
| 4. #13069404 | C2 | semidirect |
| 5. #13066728 | C2 | semidirect |
| 6. #13066706 | C2 | semidirect |
| 21. #10622205 | C4 | semidirect |
| 237. C11 | #12947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077533 | 2 |
| C2×#10622131 | 2 |
| C2×#10622205 | 2 |
| #13069404 | 2 |
| #13066728 | 2 |
| #13066706 | 2 |
| C11×#2143 | 2 |
| #12947 | 11 |