Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
466 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#10622201 | C2 | semidirect |
| 2. #13070352 | C2 | semidirect |
| 3. #13070344 | C2 | semidirect |
| 4. #13070332 | C2 | semidirect |
| 5. #13070221 | C2 | semidirect |
| 6. #13068740 | C2 | semidirect |
| 13. C11×#495 | C4 | semidirect |
| 14. C11×#493 | C4 | semidirect |
| 64. #66876 | D4 | semidirect |
| 66. C2×C11⋊C16 | D4 | semidirect |
| 166. #495 | Dic11 | semidirect |
| 167. #493 | Dic11 | semidirect |
| 291. C11 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622201 | 2 |
| #13070352 | 2 |
| #13070344 | 2 |
| #13070332 | 2 |
| #13070221 | 2 |
| #13068740 | 2 |
| C11×#3155 | 2 |
| #13215 | 11 |