Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
616 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063299 | C2 | semidirect |
| 3. #14583135 | C2 | direct (N × H) |
| 4. C2×#13063259 | C2 | semidirect |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C23×C8×C43 | C2 | semidirect |
| 10. C2×D344 | C22 | semidirect |
| 12. #13063299 | C22 | semidirect |
| 15. #13063259 | C22 | semidirect |
| 16. #13063247 | C22 | semidirect |
| 21. C22×C8×C43 | C22 | semidirect |
| 39. C2×C8×C43 | D4 | semidirect |
| 48. C23×C43 | D8 | semidirect |
| 71. C8×C43 | C2×D4 | semidirect |
| 77. C22×C43 | C2×D8 | semidirect |
| 91. C2×C43 | #466 | semidirect |
| 97. C23×C8 | D43 | semidirect |
| 102. C43 | C2×#466 | semidirect |
| 111. C22×C8 | C2×D43 | semidirect |
| 136. C2×C8 | C22⋊D43 | semidirect |
| 148. C23 | D344 | semidirect |
| 167. C8 | C2×C22⋊D43 | semidirect |
| 177. C22 | C2×D344 | semidirect |
| 187. C2 | #14583135 | direct (N × H) |