Finite Group DatabasebetaFinite Group DatabasebetaOrder 1472.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#67290 | C2 | semidirect |
| 2. C2×D4×D23 | C2 | semidirect |
| 3. C2×D8×C23 | C2 | semidirect |
| 4. C2×#67273 | C2 | semidirect |
| 5. C2×#67272 | C2 | semidirect |
| 6. #10625082 | C2 | direct (N × H) |
| 7. C2×#67263 | C2 | semidirect |
| 8. C2×#67262 | C2 | semidirect |
| 11. C2×D4×C23 | C22 | semidirect |
| 16. #67290 | C22 | semidirect |
| 18. D4×D23 | C22 | semidirect |
| 21. C2×Dic46 | C22 | semidirect |
| 22. D8×C23 | C22 | semidirect |
| 23. C2×C8×C23 | C22 | semidirect |
| 24. #67273 | C22 | semidirect |
| 25. #67272 | C22 | semidirect |
| 26. C2×C23⋊C8 | C22 | semidirect |
| 27. #67263 | C22 | semidirect |
| 28. #67262 | C22 | semidirect |
| 38. D4×C23 | C23 | semidirect |
| 50. Dic46 | C23 | semidirect |
| 51. C8×C23 | C23 | semidirect |
| 52. C23⋊C8 | C23 | semidirect |
| 70. C2×C23 | AGL(1,ℤ/8) | semidirect |
| 80. C2×D8 | D23 | semidirect |
| 82. C23 | C2×AGL(1,ℤ/8) | semidirect |
| 93. C2×D4 | C2×D23 | semidirect |
| 99. D8 | C2×D23 | semidirect |
| 102. C2×C8 | C2×D23 | semidirect |
| 118. D4 | C22×D23 | semidirect |
| 126. C8 | C22×D23 | semidirect |
| 145. C2 | #10625082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#67290 | 2 |
| C2×D4×D23 | 2 |
| C2×D8×C23 | 2 |
| C2×#67273 | 2 |
| C2×#67272 | 2 |
| #10625082 | 2 |
| C2×#67263 | 2 |
| C2×#67262 | 2 |
| C2×AGL(1,ℤ/8) | 23 |