Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
498 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 498 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 |
|---|---|---|
| 2. #13070351 | C2 | semidirect |
| 3. #13070332 | C2 | semidirect |
| 4. #13069514 | C2 | semidirect |
| 5. #13066717 | C2 | semidirect |
| 6. #13066702 | C2 | semidirect |
| 7. C11×#2948 | C2 | semidirect |
| 16. C2×#66891 | C4 | semidirect |
| 19. C2×#66890 | C4 | semidirect |
| 43. C2×Dic44 | C2×C4 | semidirect |
| 48. C2×D88 | C2×C4 | semidirect |
| 65. C2×C11⋊C16 | C2×C4 | semidirect |
| 117. #2948 | D11 | semidirect |
| 288. C11 | #13033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622760 | 2 |
| #13070351 | 2 |
| #13070332 | 2 |
| #13069514 | 2 |
| #13066717 | 2 |
| #13066702 | 2 |
| C11×#2948 | 2 |
| #13033 | 11 |