Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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×#10621884 | C2 | semidirect |
| 2. C2×#10621882 | C2 | semidirect |
| 3. #13063299 | C2 | semidirect |
| 4. #13063249 | C2 | semidirect |
| 5. #13063246 | C2 | semidirect |
| 6. C22⋊(C43⋊C8) | C2 | semidirect |
| 7. C2×#41×C43 | C2 | semidirect |
| 27. Q8×C43 | D4 | semidirect |
| 30. D4×C43 | D4 | semidirect |
| 65. C43 | #449 | semidirect |
| 66. C2×#41 | D43 | semidirect |
| 92. Q8 | C22⋊D43 | semidirect |
| 98. D4 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621884 | 2 |
| C2×#10621882 | 2 |
| #13063299 | 2 |
| #13063249 | 2 |
| #13063246 | 2 |
| C22⋊(C43⋊C8) | 2 |
| C2×#41×C43 | 2 |
| #449 | 43 |