Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C7×C13 | C3×C4 |
| prime radical | C3×D5×#63270 | C2 |
| cosocle | C3×C7×D5×C13 | C2×C3 |
| LCS | G ▷ C3×C5×C7×C13 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×C3⋊#63120 | C3 | semidirect |
| 4. C3×C5×#63270 | C4 | semidirect |
| 12. C3×C5×C7×C13 | C3×C4 | semidirect |
| 14. C5×#63270 | Dic3 | semidirect |
| 20. C3×#63270 | AGL(1,𝔽5) | semidirect |
| 21. C3⋊#63120 | ΓL(1,𝔽8) | semidirect |
| 29. C5×C7×C13 | C3×Dic3 | semidirect |
| 37. C3×C7×C13 | C3×AGL(1,𝔽5) | semidirect |
| 39. #63270 | ΓL(1,𝔽16) | semidirect |
| 46. C3×C5×C13 | C4×ΓL(1,𝔽8) | semidirect |
| 57. C3×C5×C7 | Dic13⋊C3 | semidirect |
| 60. C7×C13 | C3×ΓL(1,𝔽16) | semidirect |
| 68. C5×C13 | Dic3×ΓL(1,𝔽8) | semidirect |
| 77. C3×C13 | AGL(1,𝔽5)×ΓL(1,𝔽8) | semidirect |
| 81. C5×C7 | C3⋊(Dic13⋊C3) | semidirect |
| 87. C3×C7 | #63120⋊C3 | semidirect |
| 94. C3×C5 | #11763957 | semidirect |
| 96. C13 | ΓL(1,𝔽8)×ΓL(1,𝔽16) | semidirect |
| 101. C7 | C3⋊(#63120⋊C3) | semidirect |
| 105. C5 | C3⋊#11763957 | semidirect |
| 109. C3 | #19129741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D5×#63270 | 2 |
| C7×C3⋊#63120 | 3 |
| #19129741 | 3 |
| C3⋊#11763957 | 5 |
| C3⋊(#63120⋊C3) | 7 |
| ΓL(1,𝔽8)×ΓL(1,𝔽16) | 13 |