Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×#10621877 | C2 | semidirect |
| 3. #13063253 | C2 | direct (N × H) |
| 4. C2×C42×C43 | C2 | semidirect |
| 10. #10621898 | C4 | semidirect |
| 12. C2×D172 | C4 | semidirect |
| 14. C2×Dic86 | C4 | semidirect |
| 16. C42×C43 | C22 | semidirect |
| 18. #10621877 | C22 | semidirect |
| 34. D172 | C2×C4 | semidirect |
| 38. Dic86 | C2×C4 | semidirect |
| 54. C2×C43 | #104 | semidirect |
| 58. C43 | C2×#104 | semidirect |
| 61. C2×C42 | D43 | semidirect |
| 77. C42 | C2×D43 | semidirect |
| 113. C2 | #13063253 | 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 |
| C2×#10621877 | 2 |
| #13063253 | 2 |
| C2×C42×C43 | 2 |
| C2×#104 | 43 |