Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 565 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×#10621898 | C2 | semidirect |
| 2. C2×#13063347 | C2 | direct (N × H) |
| 3. C22×Dic172 | C2 | semidirect |
| 4. C22×#10621873 | C2 | semidirect |
| 5. C22×D344 | C2 | semidirect |
| 6. C23×C8×C43 | C2 | semidirect |
| 8. C2×#10621898 | C22 | semidirect |
| 13. #13063347 | C22 | direct (N × H) |
| 14. C2×Dic172 | C22 | semidirect |
| 15. C2×#10621873 | C22 | semidirect |
| 16. C2×D344 | C22 | semidirect |
| 20. C22×C8×C43 | C22 | semidirect |
| 30. #10621898 | C23 | semidirect |
| 38. C2×C8×C43 | C23 | semidirect |
| 39. Dic172 | C23 | semidirect |
| 40. D344 | C23 | semidirect |
| 41. #10621873 | C23 | semidirect |
| 62. C22×C43 | #135 | semidirect |
| 73. C2×C43 | C2×#135 | semidirect |
| 81. C23×C8 | D43 | semidirect |
| 82. C43 | C22×#135 | semidirect |
| 96. C22×C8 | C2×D43 | semidirect |
| 117. C2×C8 | C22×D43 | semidirect |
| 140. C22 | #13063347 | direct (N × H) |
| 149. C2 | C2×#13063347 | direct (N × H) |