Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
648 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#10621882 | C2 | semidirect |
| 2. C2×#13063322 | C2 | semidirect |
| 3. #14583094 | C2 | direct (N × H) |
| 4. C2×C4⋊(C43⋊C8) | C2 | semidirect |
| 5. C2×#13063245 | C2 | semidirect |
| 6. C2×C4×D4×C43 | C2 | semidirect |
| 11. C2×#10621882 | C22 | semidirect |
| 14. #13063322 | C22 | semidirect |
| 15. C4⋊(C43⋊C8) | C22 | semidirect |
| 16. #13063245 | C22 | semidirect |
| 20. C4×D4×C43 | C22 | semidirect |
| 28. C2×D4×C43 | D4 | semidirect |
| 63. D4×C43 | C2×D4 | semidirect |
| 68. C2×C4×C43 | D8 | semidirect |
| 96. C4×C43 | C2×D8 | semidirect |
| 101. C2×C43 | #459 | semidirect |
| 108. C2×C4×D4 | D43 | semidirect |
| 112. C43 | C2×#459 | semidirect |
| 124. C4×D4 | C2×D43 | semidirect |
| 142. C2×D4 | D172 | semidirect |
| 174. D4 | C2×D172 | semidirect |
| 179. C2×C4 | #10621882 | semidirect |
| 202. C4 | C2×#10621882 | semidirect |
| 207. C2 | #14583094 | direct (N × H) |