Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
234 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4⋊Dic43 | C2 | semidirect |
| 4. C43⋊#95 | C2 | semidirect |
| 5. C2×C4⋊C4×C43 | C2 | semidirect |
| 13. C2×C4×D43 | C4 | semidirect |
| 51. C2×D43 | C4⋊C4 | semidirect |
| 53. C4×C43 | C22⋊C4 | semidirect |
| 65. C43 | #380 | semidirect |
| 68. C2×C4⋊C4 | D43 | semidirect |
| 120. C4 | (C2×D43)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D43 | 2 |
| C2×C4⋊Dic43 | 2 |
| C2×(C2×D43)⋊C4 | 2 |
| C43⋊#95 | 2 |
| C2×C4⋊C4×C43 | 2 |
| #380 | 43 |