Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
740 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 155 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. C2×Q16×D43 | C2 | semidirect |
| 4. #14583057 | C2 | semidirect |
| 5. #14583056 | C2 | semidirect |
| 6. #14583055 | C2 | semidirect |
| 7. #14583054 | C2 | semidirect |
| 8. #14583053 | C2 | semidirect |
| 9. #103×D43 | C2 | semidirect |
| 11. C43×#451 | C2 | semidirect |
| 22. C2×Dic172 | C22 | semidirect |
| 23. C2×#10621885 | C22 | semidirect |
| 24. C2×#10621885 | C22 | semidirect |
| 35. #13063250 | C22 | semidirect |
| 36. #13063249 | C22 | semidirect |
| 37. #13063248 | C22 | semidirect |
| 41. C2×Q16×C43 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 100. C22×D43 | Q16 | semidirect |
| 140. C22×C43 | C2×Q16 | semidirect |
| 147. C2×D43 | C2×Q16 | semidirect |
| 165. D43 | #451 | direct (N × H) |
| 174. #451 | D43 | direct (N × H) |
| 177. C43 | C2×#451 | semidirect |
| 193. C2×Q16 | C2×D43 | semidirect |
| 207. #103 | C2×D43 | semidirect |
| 313. C22 | Q16×D43 | semidirect |