Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
792 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 792 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 |
|---|---|---|
| 1. C22×Q8×D43 | C2 | semidirect |
| 2. C2×SD16×D43 | C2 | semidirect |
| 4. #14583040 | C2 | semidirect |
| 5. #14583039 | C2 | semidirect |
| 6. #14583038 | C2 | semidirect |
| 7. #14583037 | C2 | semidirect |
| 8. #14583036 | C2 | semidirect |
| 9. #103×D43 | C2 | semidirect |
| 10. C22⋊C8×D43 | C2 | semidirect |
| 11. C43×#448 | C2 | semidirect |
| 13. C22×Dic86 | C22 | semidirect |
| 18. C2×Q8×D43 | C22 | semidirect |
| 23. C2×#10621873 | C22 | semidirect |
| 24. C2×#10621883 | C22 | semidirect |
| 25. C2×#10621884 | C22 | semidirect |
| 35. #13063250 | C22 | semidirect |
| 36. #13063249 | C22 | semidirect |
| 37. #13063248 | C22 | semidirect |
| 38. C22⋊(C43⋊C8) | C22 | semidirect |
| 39. (C2×D43)⋊C8 | C22 | semidirect |
| 40. C22×Q8×C43 | C22 | semidirect |
| 41. C2×SD16×C43 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 44. C22⋊C8×C43 | C22 | semidirect |
| 64. Q8×D43 | D4 | semidirect |
| 106. C22×D43 | SD16 | semidirect |
| 111. Q8×C43 | C2×D4 | semidirect |
| 142. Dic86 | C2×D4 | semidirect |
| 150. C22×C43 | C2×SD16 | semidirect |
| 161. C2×D43 | C2×SD16 | semidirect |
| 179. D43 | #448 | direct (N × H) |
| 188. #448 | D43 | direct (N × H) |
| 191. C43 | C2×#448 | semidirect |
| 199. C22×Q8 | C2×D43 | semidirect |
| 208. C2×SD16 | C2×D43 | semidirect |
| 221. #103 | C2×D43 | semidirect |
| 224. C22⋊C8 | C2×D43 | semidirect |
| 296. Q8 | D4×D43 | semidirect |
| 341. C22 | SD16×D43 | semidirect |