Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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×#10621882 | C2 | semidirect |
| 2. C22×C43⋊C8 | C2 | semidirect |
| 3. #13063299 | C2 | semidirect |
| 4. #13063258 | C2 | semidirect |
| 5. #13063246 | C2 | semidirect |
| 6. #13063245 | C2 | semidirect |
| 7. #121×C43 | C2 | semidirect |
| 37. C43⋊C8 | D4 | semidirect |
| 43. C22×C43 | D8 | semidirect |
| 60. C43 | #466 | semidirect |
| 64. #121 | D43 | semidirect |
| 106. C22 | #10621882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621882 | 2 |
| C22×C43⋊C8 | 2 |
| #13063299 | 2 |
| #13063258 | 2 |
| #13063246 | 2 |
| #13063245 | 2 |
| #121×C43 | 2 |
| #466 | 43 |