Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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. C23×C43⋊C8 | C2 | semidirect |
| 3. C2×#13063245 | C2 | direct (N × H) |
| 4. C22×C4⋊C4×C43 | C2 | semidirect |
| 8. C22×D172 | C4 | semidirect |
| 11. C22×C43⋊C8 | C22 | semidirect |
| 12. #13063245 | C22 | direct (N × H) |
| 16. C2×C4⋊C4×C43 | C22 | semidirect |
| 31. C2×D172 | C2×C4 | semidirect |
| 34. C4⋊C4×C43 | C23 | semidirect |
| 36. C2×C43⋊C8 | C23 | semidirect |
| 55. D172 | C22×C4 | semidirect |
| 57. C22×C43 | #102 | semidirect |
| 71. C2×C43 | C2×#102 | semidirect |
| 78. C22×C4⋊C4 | D43 | semidirect |
| 80. C43 | C22×#102 | semidirect |
| 91. C2×C4⋊C4 | C2×D43 | semidirect |
| 112. C4⋊C4 | C22×D43 | semidirect |
| 137. C22 | #13063245 | direct (N × H) |
| 147. C2 | C2×#13063245 | direct (N × H) |