Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
844 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063350 | C2 | semidirect |
| 2. C2×#13063321 | C2 | semidirect |
| 3. #14583067 | C2 | direct (N × H) |
| 4. C2×#13063252 | C2 | semidirect |
| 5. C2×#13063242 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C43 | C2 | semidirect |
| 7. C22×D172 | C22 | semidirect |
| 10. #13063350 | C22 | semidirect |
| 13. C2×#10621877 | C22 | semidirect |
| 15. #13063321 | C22 | semidirect |
| 16. C2×C4×Dic43 | C22 | semidirect |
| 17. #13063252 | C22 | semidirect |
| 18. #13063242 | C22 | semidirect |
| 21. H(5,𝔽2)×C43 | C22 | semidirect |
| 34. #41×C43 | D4 | semidirect |
| 36. C2×Q8×C43 | D4 | semidirect |
| 46. C2×D4×C43 | D4 | semidirect |
| 57. C2×D172 | C23 | semidirect |
| 61. C4×Dic43 | C23 | semidirect |
| 63. #10621877 | C23 | semidirect |
| 78. Q8×C43 | C2×D4 | semidirect |
| 85. D4×C43 | C2×D4 | semidirect |
| 124. C2×C43 | #453 | semidirect |
| 127. C2×H(5,𝔽2) | D43 | semidirect |
| 133. C43 | C2×#453 | semidirect |
| 136. H(5,𝔽2) | C2×D43 | semidirect |
| 161. #41 | C22⋊D43 | semidirect |
| 163. C2×Q8 | C22⋊D43 | semidirect |
| 179. C2×D4 | C22⋊D43 | semidirect |
| 205. Q8 | C2×C22⋊D43 | semidirect |
| 215. D4 | C2×C22⋊D43 | semidirect |
| 251. C2 | #14583067 | direct (N × H) |