Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
312 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 105 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. #14582952 | C2 | semidirect |
| 2. #14582923 | C2 | semidirect |
| 3. D4⋊(C43⋊C8) | C2 | semidirect |
| 8. C4⋊(C43⋊C8) | C22 | semidirect |
| 10. C4×C43⋊C8 | C22 | semidirect |
| 50. D4×C43 | M16 | semidirect |
| 94. C43 | #1486 | semidirect |
| 140. D4 | #10621877 | semidirect |