Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
462 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 155 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. C22×Dic88 | C2 | semidirect |
| 2. #13070933 | C2 | direct (N × H) |
| 3. C2×#10622160 | C2 | semidirect |
| 4. C2×#10622158 | C2 | semidirect |
| 5. C2×#10622137 | C2 | semidirect |
| 18. C2×Dic88 | C22 | semidirect |
| 19. #10622160 | C22 | semidirect |
| 20. #10622158 | C22 | semidirect |
| 21. #10622137 | C22 | semidirect |
| 156. C2×C11 | #2264 | semidirect |
| 185. C11 | C2×#2264 | semidirect |
| 219. C2 | #13070933 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic88 | 2 |
| #13070933 | 2 |
| C2×#10622160 | 2 |
| C2×#10622158 | 2 |
| C2×#10622137 | 2 |
| C2×C11×#508 | 2 |
| C2×#2264 | 11 |