Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
310 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 155 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. #13063290 | C2 | semidirect |
| 3. #13063287 | C2 | semidirect |
| 4. (C22⋊D43)⋊C4 | C2 | semidirect |
| 5. #13063282 | C2 | semidirect |
| 6. C2×C4×Dic43 | C2 | semidirect |
| 7. C42×D43 | C2 | semidirect |
| 8. #117×C43 | C2 | semidirect |
| 12. #10621898 | C4 | semidirect |
| 28. C2×C4×C43 | C2×C4 | semidirect |
| 32. C22⋊D43 | C2×C4 | semidirect |
| 37. D172 | C2×C4 | semidirect |
| 39. C4×D43 | C2×C4 | semidirect |
| 40. Dic86 | C2×C4 | semidirect |
| 51. Dic43 | #41 | semidirect |
| 57. C43 | C4×#41 | semidirect |
| 63. #117 | D43 | semidirect |
| 94. C2×C4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063290 | 2 |
| #13063287 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063282 | 2 |
| C2×C4×Dic43 | 2 |
| C42×D43 | 2 |
| #117×C43 | 2 |
| C4×#41 | 43 |