Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. C2×C4×D172 | C2 | semidirect |
| 3. C4×D344 | C2 | direct (N × H) |
| 4. C2×#13063259 | C2 | semidirect |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C2×C4×C8×C43 | C2 | semidirect |
| 9. C2×D344 | C4 | direct (N × H) |
| 12. C4×D172 | C22 | semidirect |
| 15. #13063259 | C22 | semidirect |
| 16. #13063247 | C22 | semidirect |
| 20. C4×C8×C43 | C22 | semidirect |
| 28. C2×D172 | C2×C4 | semidirect |
| 33. C2×C8×C43 | C2×C4 | semidirect |
| 41. D344 | C2×C4 | direct (N × H) |
| 48. C2×C4×C43 | D8 | semidirect |
| 59. D172 | C22×C4 | semidirect |
| 62. C8×C43 | C22×C4 | semidirect |
| 73. C4×C43 | C2×D8 | semidirect |
| 78. C2×C43 | C4×D8 | semidirect |
| 88. C2×C4×C8 | D43 | semidirect |
| 89. C43 | C2×C4×D8 | semidirect |
| 103. C4×C8 | C2×D43 | semidirect |
| 117. C2×C8 | C4×D43 | semidirect |
| 137. C2×C4 | D344 | direct (N × H) |
| 145. C8 | C2×C4×D43 | semidirect |
| 157. C4 | C2×D344 | direct (N × H) |
| 161. C2 | C4×D344 | direct (N × H) |