Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
172 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×D21 |
| commutator, socle, cosocle | C2×C32×C7 | C23 |
| Fitting | C32×C4×C7 | C22 |
| hypercenter | C4 | D3×D21 |
| hypocenter | C32×C7 | #41 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #92722 | C2 | semidirect |
| 2. C3×C4×D21 | C2 | semidirect |
| 3. C3×C7×D12 | C2 | semidirect |
| 4. #92688 | C2 | semidirect |
| 5. D3×Dic21 | C2 | semidirect |
| 16. C4×D21 | D3 | semidirect |
| 20. C7×D12 | D3 | semidirect |
| 42. C3×D12 | D7 | semidirect |
| 46. C32×C7 | #41 | semidirect |
| 76. D12 | D21 | semidirect |
| 83. C3×C7 | #235 | semidirect |
| 84. C3×C7 | #237 | semidirect |
| 104. C32 | #1159 | semidirect |
| 110. C7 | #3795 | semidirect |
| 124. C3 | #66676 | semidirect |
| 125. C3 | #66730 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #92722 | 2 |
| C3×C4×D21 | 2 |
| C3×C7×D12 | 2 |
| #92688 | 2 |
| D3×Dic21 | 2 |
| #66730 | 3 |
| #66676 | 3 |
| #3795 | 7 |