Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 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 |
|---|---|---|
| 2. C23×Dic86 | C2 | semidirect |
| 3. C2×#13063358 | C2 | direct (N × H) |
| 4. C22×Dic172 | C2 | semidirect |
| 5. C22×#10621873 | C2 | semidirect |
| 6. C22×M16×C43 | C2 | semidirect |
| 13. C22×Dic86 | C22 | semidirect |
| 18. #13063358 | C22 | direct (N × H) |
| 19. C2×Dic172 | C22 | semidirect |
| 20. C2×#10621873 | C22 | semidirect |
| 22. C2×M16×C43 | C22 | semidirect |
| 45. C2×Dic86 | C23 | semidirect |
| 46. M16×C43 | C23 | semidirect |
| 48. Dic172 | C23 | semidirect |
| 49. #10621873 | C23 | semidirect |
| 74. C22×C43 | #137 | semidirect |
| 86. C2×C43 | C2×#137 | semidirect |
| 94. C22×M16 | D43 | semidirect |
| 95. C43 | C22×#137 | semidirect |
| 111. C2×M16 | C2×D43 | semidirect |
| 137. M16 | C22×D43 | semidirect |
| 165. C22 | #13063358 | direct (N × H) |
| 175. C2 | C2×#13063358 | direct (N × H) |