Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#10621883 | C2 | semidirect |
| 2. C22×C43⋊C8 | C2 | semidirect |
| 3. #13063304 | C2 | semidirect |
| 4. #13063256 | C2 | semidirect |
| 5. #13063248 | C2 | semidirect |
| 6. #13063246 | C2 | semidirect |
| 36. C43⋊C8 | D4 | semidirect |
| 42. C22×C43 | SD16 | semidirect |
| 56. C43 | #465 | semidirect |
| 98. C22 | #10621883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621883 | 2 |
| C22×C43⋊C8 | 2 |
| #13063304 | 2 |
| #13063256 | 2 |
| #13063248 | 2 |
| #13063246 | 2 |
| #121×C43 | 2 |
| #465 | 43 |