Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #13068662 | C2 | semidirect |
| 4. #13066736 | C2 | semidirect |
| 5. C11×#1812 | C2 | semidirect |
| 8. C2×#66954 | C4 | semidirect |
| 13. #10622742 | C4 | semidirect |
| 16. #10622731 | C4 | semidirect |
| 20. C2×#66879 | C4 | semidirect |
| 125. #1812 | D11 | semidirect |
| 306. C11 | #12808 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13077332 | 2 |
| #13070279 | 2 |
| #13068662 | 2 |
| #13066736 | 2 |
| C11×#1812 | 2 |
| #12808 | 11 |