Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
792 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#10621883 | C2 | semidirect |
| 4. #14583036 | C2 | direct (N × H) |
| 5. C2×#13063250 | C2 | semidirect |
| 6. C2×#13063249 | C2 | semidirect |
| 7. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 14. C2×Q8×D43 | C22 | semidirect |
| 19. C2×#10621883 | C22 | semidirect |
| 25. #13063250 | C22 | semidirect |
| 26. #13063249 | C22 | semidirect |
| 27. (C2×D43)⋊C8 | C22 | semidirect |
| 31. C2×SD16×C43 | C22 | semidirect |
| 37. C2×Q8×C43 | D4 | semidirect |
| 63. C2×Dic86 | D4 | semidirect |
| 81. C22×D43 | SD16 | semidirect |
| 85. Q8×C43 | C2×D4 | semidirect |
| 109. Dic86 | C2×D4 | semidirect |
| 123. C2×D43 | C2×SD16 | semidirect |
| 133. C2×C43 | #448 | semidirect |
| 140. C22×SD16 | D43 | semidirect |
| 146. C43 | C2×#448 | semidirect |
| 161. C2×SD16 | C2×D43 | semidirect |
| 184. C2×Q8 | C22⋊D43 | semidirect |
| 227. Q8 | C2×C22⋊D43 | semidirect |
| 271. C2 | #14583036 | direct (N × H) |