Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic86 | C2 | semidirect |
| 3. #13063358 | C2 | direct (N × H) |
| 4. C2×Dic172 | C2 | semidirect |
| 5. C2×#10621873 | C2 | semidirect |
| 6. C2×M16×C43 | C2 | semidirect |
| 18. C2×Dic86 | C22 | semidirect |
| 19. M16×C43 | C22 | semidirect |
| 21. Dic172 | C22 | semidirect |
| 22. #10621873 | C22 | semidirect |
| 53. C2×C43 | #137 | semidirect |
| 57. C43 | C2×#137 | semidirect |
| 63. C2×M16 | D43 | semidirect |
| 78. M16 | C2×D43 | semidirect |
| 111. C2 | #13063358 | 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 |
| C22×Dic86 | 2 |
| #13063358 | 2 |
| C2×Dic172 | 2 |
| C2×#10621873 | 2 |
| C2×M16×C43 | 2 |
| C2×#137 | 43 |