Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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×#10621883 | C2 | semidirect |
| 2. C2×C4×Dic86 | C2 | semidirect |
| 3. #14583096 | C2 | direct (N × H) |
| 4. C2×C4⋊(C43⋊C8) | C2 | semidirect |
| 5. C2×#13063246 | C2 | semidirect |
| 9. C2×#10621883 | C22 | semidirect |
| 12. C4×Dic86 | C22 | semidirect |
| 16. C4⋊(C43⋊C8) | C22 | semidirect |
| 17. #13063246 | C22 | semidirect |
| 40. C2×Dic86 | D4 | semidirect |
| 62. C2×C4×C43 | SD16 | semidirect |
| 75. Dic86 | C2×D4 | semidirect |
| 87. C4×C43 | C2×SD16 | semidirect |
| 94. C2×C43 | #460 | semidirect |
| 104. C43 | C2×#460 | semidirect |
| 167. C2×C4 | #10621883 | semidirect |
| 187. C4 | C2×#10621883 | semidirect |
| 191. C2 | #14583096 | direct (N × H) |