Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 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×D4×D43 | C2 | semidirect |
| 2. C2×#10621882 | C2 | semidirect |
| 3. #13063296 | C2 | semidirect |
| 4. #13063247 | C2 | semidirect |
| 5. #13063246 | C2 | semidirect |
| 6. (C2×D43)⋊C8 | C2 | semidirect |
| 7. C2×D8×C43 | C2 | semidirect |
| 10. C2×D4×C43 | C22 | semidirect |
| 18. C2×C8×C43 | C22 | semidirect |
| 21. C4⋊Dic43 | C22 | semidirect |
| 22. C2×C43⋊C8 | C22 | semidirect |
| 33. D4×C43 | D4 | semidirect |
| 40. D172 | D4 | semidirect |
| 58. C2×D43 | D8 | semidirect |
| 71. C43 | #447 | semidirect |
| 74. C2×D8 | D43 | semidirect |
| 86. C2×D4 | C2×D43 | semidirect |
| 91. C2×C8 | C2×D43 | semidirect |
| 108. D4 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D43 | 2 |
| C2×#10621882 | 2 |
| #13063296 | 2 |
| #13063247 | 2 |
| #13063246 | 2 |
| (C2×D43)⋊C8 | 2 |
| C2×D8×C43 | 2 |
| #447 | 43 |