Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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. #13063333 | C2 | direct (N × H) |
| 3. C2×#10621872 | C2 | semidirect |
| 4. C22×C43⋊C8 | C2 | semidirect |
| 5. C2×C8×D43 | C2 | semidirect |
| 6. C2×M16×C43 | C2 | semidirect |
| 14. M16×C43 | C22 | semidirect |
| 18. C2×C43⋊C8 | C22 | semidirect |
| 19. #10621872 | C22 | semidirect |
| 20. C8×D43 | C22 | semidirect |
| 46. C2×C43 | #131 | semidirect |
| 50. C43 | C2×#131 | semidirect |
| 54. C2×M16 | D43 | semidirect |
| 65. M16 | C2×D43 | semidirect |
| 97. C2 | #13063333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063333 | 2 |
| C2×#10621872 | 2 |
| C22×C43⋊C8 | 2 |
| C2×C8×D43 | 2 |
| C2×M16×C43 | 2 |
| C2×#131 | 43 |