Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
440 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 149 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×D344 | C2 | semidirect |
| 2. C2×#13063266 | C2 | direct (N × H) |
| 3. C22×C43⋊C16 | C2 | semidirect |
| 4. C22×D8×C43 | C2 | semidirect |
| 7. C2×D344 | C22 | semidirect |
| 8. #13063266 | C22 | direct (N × H) |
| 9. C2×C43⋊C16 | C22 | semidirect |
| 12. C2×D8×C43 | C22 | semidirect |
| 22. D8×C43 | C23 | semidirect |
| 26. D344 | C23 | semidirect |
| 27. C43⋊C16 | C23 | semidirect |
| 43. C22×C43 | D16 | semidirect |
| 51. C2×C43 | C2×D16 | semidirect |
| 55. C22×D8 | D43 | semidirect |
| 58. C43 | C22×D16 | semidirect |
| 64. C2×D8 | C2×D43 | semidirect |
| 78. D8 | C22×D43 | semidirect |
| 99. C22 | #13063266 | direct (N × H) |
| 105. C2 | C2×#13063266 | direct (N × H) |