Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×Dic86 | C2 | semidirect |
| 3. #13063290 | C2 | semidirect |
| 4. D4×Dic43 | C2 | semidirect |
| 5. C4×C22⋊D43 | C2 | semidirect |
| 6. (C22⋊D43)⋊C4 | C2 | semidirect |
| 7. #13063282 | C2 | semidirect |
| 8. #13063281 | C2 | semidirect |
| 9. C2×Dic43⋊C4 | C2 | semidirect |
| 10. C4⋊C4×D43 | C2 | semidirect |
| 11. C4×D4×C43 | C2 | semidirect |
| 17. #10621900 | C4 | semidirect |
| 38. D4×C43 | C2×C4 | semidirect |
| 44. C22⋊D43 | C2×C4 | semidirect |
| 46. C2×Dic43 | C2×C4 | semidirect |
| 53. C4×D43 | C2×C4 | semidirect |
| 54. Dic86 | C2×C4 | semidirect |
| 77. C43 | #520 | semidirect |
| 84. C4×D4 | D43 | semidirect |
| 117. D4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621900 | 2 |
| C4×Dic86 | 2 |
| #13063290 | 2 |
| D4×Dic43 | 2 |
| C4×C22⋊D43 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063282 | 2 |
| #13063281 | 2 |
| C2×Dic43⋊C4 | 2 |
| C4⋊C4×D43 | 2 |
| C4×D4×C43 | 2 |
| #520 | 43 |