Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×#10621877 | C2 | semidirect |
| 3. C2×#13063253 | C2 | direct (N × H) |
| 4. C22×C42×C43 | C2 | semidirect |
| 7. C2×#10621898 | C4 | semidirect |
| 9. C22×Dic86 | C4 | semidirect |
| 10. C22×D172 | C4 | semidirect |
| 14. C2×#10621877 | C22 | semidirect |
| 16. #13063253 | C22 | direct (N × H) |
| 20. C2×C42×C43 | C22 | semidirect |
| 37. #10621898 | C2×C4 | semidirect |
| 40. C2×D172 | C2×C4 | semidirect |
| 44. C2×Dic86 | C2×C4 | semidirect |
| 46. C42×C43 | C23 | semidirect |
| 48. #10621877 | C23 | semidirect |
| 71. D172 | C22×C4 | semidirect |
| 75. Dic86 | C22×C4 | semidirect |
| 79. C22×C43 | #104 | semidirect |
| 94. C2×C43 | C2×#104 | semidirect |
| 99. C22×C42 | D43 | semidirect |
| 101. C43 | C22×#104 | semidirect |
| 116. C2×C42 | C2×D43 | semidirect |
| 146. C42 | C22×D43 | semidirect |
| 178. C22 | #13063253 | direct (N × H) |
| 191. C2 | C2×#13063253 | direct (N × H) |