Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. #13063350 | C2 | semidirect |
| 2. C2×#10621882 | C2 | semidirect |
| 3. #13063332 | C2 | semidirect |
| 4. #13063260 | C2 | semidirect |
| 5. #13063242 | C2 | semidirect |
| 6. #13063241 | C2 | semidirect |
| 7. AGL(1,ℤ/8)×C43 | C2 | semidirect |
| 54. C43 | #472 | semidirect |
| 56. AGL(1,ℤ/8) | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063350 | 2 |
| C2×#10621882 | 2 |
| #13063332 | 2 |
| #13063260 | 2 |
| #13063242 | 2 |
| #13063241 | 2 |
| AGL(1,ℤ/8)×C43 | 2 |
| #472 | 43 |