Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
302 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10622143 | C2 | semidirect |
| 3. #13066804 | C2 | direct (N × H) |
| 4. C2×C11×M64 | C2 | semidirect |
| 8. C2×Dic88 | C4 | semidirect |
| 11. #10622517 | C4 | semidirect |
| 14. C2×D176 | C4 | semidirect |
| 16. C11×M64 | C22 | semidirect |
| 19. #10622143 | C22 | semidirect |
| 39. Dic88 | C2×C4 | semidirect |
| 43. D176 | C2×C4 | semidirect |
| 75. C2×M64 | D11 | semidirect |
| 112. M64 | C2×D11 | semidirect |
| 155. C2×C11 | #1418 | semidirect |
| 186. C11 | C2×#1418 | semidirect |
| 225. C2 | #13066804 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622517 | 2 |
| C2×#10622143 | 2 |
| #13066804 | 2 |
| C2×C11×M64 | 2 |
| C2×#1418 | 11 |