Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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. C22×#10621884 | C2 | semidirect |
| 2. C22×#10621882 | C2 | semidirect |
| 3. C2×#13063322 | C2 | semidirect |
| 4. #14583289 | C2 | direct (N × H) |
| 5. C2×#13063236 | C2 | semidirect |
| 6. C2×#124×C43 | C2 | semidirect |
| 10. C2×#10621884 | C22 | semidirect |
| 12. C2×#10621882 | C22 | semidirect |
| 15. #13063322 | C22 | semidirect |
| 16. #13063236 | C22 | semidirect |
| 20. #124×C43 | C22 | semidirect |
| 45. C2×C43⋊C8 | D4 | semidirect |
| 69. C43⋊C8 | C2×D4 | semidirect |
| 85. C2×C43 | #496 | semidirect |
| 92. C2×#124 | D43 | semidirect |
| 95. C43 | C2×#496 | semidirect |
| 108. #124 | C2×D43 | semidirect |
| 174. C2 | #14583289 | direct (N × H) |