Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
112 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 36 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. C7×C3⋊#63121 | C3 | semidirect |
| 4. C3×C5×C7×C13⋊C3 | C4 | semidirect |
| 9. C3⋊(#63121⋊C3) | C7 | direct (N × H) |
| 12. C3×C5×C7×C13 | C3×C4 | semidirect |
| 14. C5×C7×C13⋊C3 | Dic3 | semidirect |
| 20. C3×C7×C13⋊C3 | AGL(1,𝔽5) | semidirect |
| 21. C3⋊#63121 | C3×C7 | semidirect |
| 24. C3×C5×C13⋊C3 | C4×C7 | semidirect |
| 29. C5×C7×C13 | C3×Dic3 | semidirect |
| 37. C3×C7×C13 | C3×AGL(1,𝔽5) | semidirect |
| 39. C7×C13⋊C3 | ΓL(1,𝔽16) | semidirect |
| 46. C3×C5×C13 | C3×C4×C7 | semidirect |
| 48. C5×C13⋊C3 | C7×Dic3 | semidirect |
| 56. C3×C13⋊C3 | C7×AGL(1,𝔽5) | semidirect |
| 59. C3×C5×C7 | AGL(1,𝔽13) | semidirect |
| 60. C7×C13 | C3×ΓL(1,𝔽16) | semidirect |
| 68. C5×C13 | C3×C7×Dic3 | semidirect |
| 77. C3×C13 | C3×C7×AGL(1,𝔽5) | semidirect |
| 79. C13⋊C3 | C7×ΓL(1,𝔽16) | semidirect |
| 81. C5×C7 | C3⋊AGL(1,𝔽13) | semidirect |
| 89. C3×C7 | #63121⋊C3 | semidirect |
| 94. C3×C5 | C7×AGL(1,𝔽13) | semidirect |
| 96. C13 | C3×C7×ΓL(1,𝔽16) | semidirect |
| 101. C7 | C3⋊(#63121⋊C3) | direct (N × H) |
| 105. C5 | C7×C3⋊AGL(1,𝔽13) | semidirect |
| 109. C3 | C7×#63121⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C5⋊(D13⋊C3) | 2 |
| C7×C3⋊#63121 | 3 |
| C7×#63121⋊C3 | 3 |
| C7×C3⋊AGL(1,𝔽13) | 5 |
| C3⋊(#63121⋊C3) | 7 |
| C3×C7×ΓL(1,𝔽16) | 13 |