Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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×#10621873 | C2 | semidirect |
| 2. C2×#13063325 | C2 | semidirect |
| 4. #14583272 | C2 | direct (N × H) |
| 5. C2×C4×C8×C43 | C2 | semidirect |
| 10. C2×#10621873 | C22 | semidirect |
| 12. #13063325 | C22 | semidirect |
| 18. C4×C8×C43 | C22 | semidirect |
| 31. C2×C8×C43 | D4 | semidirect |
| 41. C2×C4×C43 | SD16 | semidirect |
| 53. C8×C43 | C2×D4 | semidirect |
| 61. C4×C43 | C2×SD16 | semidirect |
| 65. C2×C43 | #492 | semidirect |
| 73. C2×C4×C8 | D43 | semidirect |
| 74. C43 | C2×#492 | semidirect |
| 87. C4×C8 | C2×D43 | semidirect |
| 101. C2×C8 | D172 | semidirect |
| 117. C2×C4 | #10621873 | semidirect |
| 122. C8 | C2×D172 | semidirect |
| 131. C4 | C2×#10621873 | semidirect |
| 134. C2 | #14583272 | direct (N × H) |