Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
140 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 1. C2×D344 | C2 | semidirect |
| 2. C2×#10621882 | C2 | semidirect |
| 3. #13063321 | C2 | semidirect |
| 4. #13063287 | C2 | semidirect |
| 5. Dic43⋊C8 | C2 | semidirect |
| 6. #13063245 | C2 | semidirect |
| 7. #102×C43 | C2 | semidirect |
| 35. D172 | D4 | semidirect |
| 53. Dic43 | D8 | semidirect |
| 61. C43 | #459 | semidirect |
| 68. #102 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D344 | 2 |
| C2×#10621882 | 2 |
| #13063321 | 2 |
| #13063287 | 2 |
| Dic43⋊C8 | 2 |
| #13063245 | 2 |
| #102×C43 | 2 |
| #459 | 43 |