Finite Group Databasebeta

Non-abelian indecomposable groups of order 216

← order 215 order 217 →

65 non-abelian indecomposable groups of order 216.

Groups that are neither abelian nor a non-trivial direct product.

SmallGroupsgroup
(216, 1)C27⋊C8 #6164
(216, 3)Q8⋊C27 #6166
(216, 4)Dic54 #6167
(216, 6)D108 #6169
(216, 8)#6171
(216, 14)(C3⋊(C3⋊C8))⋊C3 #6177
(216, 15)3−1+2⋊C8 #6178
(216, 16)C3⋊(C9⋊C8) #6179
(216, 17)#6180
(216, 21)(C22⋊C27)⋊C2 #6184
(216, 25)#6188
(216, 26)#6189
(216, 28)(C3⋊D9)⋊C4 #6191
(216, 29)#6192
(216, 31)#6194
(216, 32)#6195
(216, 33)#6196
(216, 34)((C3⋊D3)⋊C3)⋊C4 #6197
(216, 35)#6198
(216, 36)#6199
(216, 37)#6200
(216, 39)C9⋊SL(2,𝔽3) #6202
(216, 41)#6204
(216, 42)Q8⋊H(3,𝔽3) #6205
(216, 49)#634⋊C3 #6212
(216, 51)C4⋊((C3⋊D3)⋊C3) #6214
(216, 52)3−1+2⋊Q8 #6215
(216, 54)C4⋊AGL(1,ℤ/9) #6217
(216, 60)#638⋊C3 #6223
(216, 62)#611⋊C3 #6225
(216, 63)#6226
(216, 65)C4⋊(C3⋊D9) #6228
(216, 66)#6229
(216, 68)C4⋊#272 #6231
(216, 70)#6233
(216, 72)#6235
(216, 84)C3⋊(C3⋊(C3⋊C8)) #6247
(216, 86)#6249
(216, 87)#1088⋊C2 #6250
(216, 88)SU(3,𝔽2) #6251
(216, 90)((C22⋊C9)⋊C2)⋊C3 #6253
(216, 92)(C3⋊S4)⋊C3 #6255
(216, 93)C9⋊S4 #6256
(216, 94)C3⋊((C22⋊C9)⋊C2) #6257
(216, 95)#6258
(216, 96)D9⋊A4 #6259
(216, 99)(C3⋊D3)⋊A4 #6262
(216, 118)C3⋊#622 #6281
(216, 126)#6289
(216, 127)#6290
(216, 128)#6291
(216, 129)#6292
(216, 130)#6293
(216, 131)#6294
(216, 132)#6295
(216, 133)#6296
(216, 145)#6308
(216, 147)C4⋊(C3⋊(C3⋊D3)) #6310
(216, 149)#6312
(216, 153)PSU(3,𝔽2)⋊C3 #6316
(216, 155)C3⋊AGL(1,𝔽9) #6318
(216, 158)D32⋊D3 #6321
(216, 159)#157⋊D3 #6322
(216, 161)C3⋊PSU(3,𝔽2) #6324
(216, 165)C3⋊(C3⋊S4) #6328

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