Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #14583217 | C2 | direct (N × H) |
| 3. C2×#13063256 | C2 | semidirect |
| 4. C2×#13063245 | C2 | semidirect |
| 5. C2×C22⋊(C43⋊C8) | C2 | semidirect |
| 6. C22×C4⋊C4×C43 | C2 | semidirect |
| 14. #13063256 | C22 | semidirect |
| 15. #13063245 | C22 | semidirect |
| 16. C22⋊(C43⋊C8) | C22 | semidirect |
| 22. C2×C4⋊C4×C43 | C22 | semidirect |
| 91. C2×C43 | #481 | semidirect |
| 97. C22×C4⋊C4 | D43 | semidirect |
| 102. C43 | C2×#481 | semidirect |
| 114. C2×C4⋊C4 | C2×D43 | semidirect |
| 187. C2 | #14583217 | direct (N × H) |