Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#13063236 | C2 | semidirect |
| 4. #14582661 | C2 | semidirect |
| 5. C4×C4⋊C4×C43 | C2 | semidirect |
| 10. C4×D172 | C4 | semidirect |
| 13. #13063245 | C4 | semidirect |
| 32. C4⋊C4×C43 | C2×C4 | semidirect |
| 41. C2×C43⋊C8 | C2×C4 | semidirect |
| 64. D172 | C42 | semidirect |
| 94. C4×C4⋊C4 | D43 | semidirect |
| 96. C43 | #1762 | semidirect |
| 128. C4⋊C4 | C4×D43 | semidirect |