Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#10621898 | C2 | semidirect |
| 2. C2×#10621883 | C2 | semidirect |
| 3. C2×#10621882 | C2 | semidirect |
| 4. #13063248 | C2 | semidirect |
| 5. #13063245 | C2 | semidirect |
| 6. C22⋊(C43⋊C8) | C2 | semidirect |
| 7. #121×C43 | C2 | semidirect |
| 37. D172 | D4 | semidirect |
| 40. Dic86 | D4 | semidirect |
| 65. C43 | #449 | semidirect |
| 69. #121 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| C2×#10621883 | 2 |
| C2×#10621882 | 2 |
| #13063248 | 2 |
| #13063245 | 2 |
| C22⋊(C43⋊C8) | 2 |
| #121×C43 | 2 |
| #449 | 43 |