Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #13063284 | C2 | semidirect |
| 3. #13063251 | C2 | semidirect |
| 4. C2×M16×C43 | C2 | semidirect |
| 9. #10621898 | C4 | semidirect |
| 11. C2×D172 | C4 | semidirect |
| 13. C2×Dic86 | C4 | semidirect |
| 15. M16×C43 | C22 | semidirect |
| 19. C4×Dic43 | C22 | semidirect |
| 57. C43 | #421 | semidirect |
| 59. C2×M16 | D43 | semidirect |
| 72. M16 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| #13063284 | 2 |
| #13063251 | 2 |
| C2×M16×C43 | 2 |
| #421 | 43 |