Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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×C4×D172 | C2 | semidirect |
| 3. #14583091 | C2 | direct (N × H) |
| 4. C2×C4⋊(C43⋊C8) | C2 | semidirect |
| 5. C2×#13063246 | C2 | semidirect |
| 6. C2×#127×C43 | C2 | semidirect |
| 10. C2×#10621882 | C22 | semidirect |
| 13. C4×D172 | C22 | semidirect |
| 16. C4⋊(C43⋊C8) | C22 | semidirect |
| 17. #13063246 | C22 | semidirect |
| 22. #127×C43 | C22 | semidirect |
| 40. C2×D172 | D4 | semidirect |
| 67. C2×C4×C43 | D8 | semidirect |
| 78. D172 | C2×D4 | semidirect |
| 95. C4×C43 | C2×D8 | semidirect |
| 101. C2×C43 | #459 | semidirect |
| 107. C2×#127 | D43 | semidirect |
| 112. C43 | C2×#459 | semidirect |
| 122. #127 | C2×D43 | semidirect |
| 179. C2×C4 | #10621882 | semidirect |
| 202. C4 | C2×#10621882 | semidirect |
| 207. C2 | #14583091 | direct (N × H) |