Finite Group DatabasebetaFinite Group Databasebeta19 non-abelian indecomposable groups of order 72.
Groups that are neither abelian nor a non-trivial direct product.
| SmallGroups | group |
|---|---|
| (72, 1) | C9⋊C8 #604 |
| (72, 3) | Q8⋊C9 #606 |
| (72, 4) | Dic18 #607 |
| (72, 6) | D36 #609 |
| (72, 8) | #611 |
| (72, 13) | C3⋊(C3⋊C8) #616 |
| (72, 15) | (C22⋊C9)⋊C2 #618 |
| (72, 19) | #622 |
| (72, 21) | #624 |
| (72, 22) | #625 |
| (72, 23) | #626 |
| (72, 24) | #627 |
| (72, 31) | #634 |
| (72, 33) | C4⋊(C3⋊D3) #636 |
| (72, 35) | #638 |
| (72, 39) | AGL(1,𝔽9) #642 |
| (72, 40) | GO+(4,𝔽2) #643 |
| (72, 41) | PSU(3,𝔽2) #644 |
| (72, 43) | C3⋊S4 #646 |