Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D21 |
| commutator, cosocle | C2×C32×C7 | C23 |
| Frattini | C2 | C2×D3×D21 |
| Fitting, socle, prime radical | C22×C32×C7 | C22 |
| hypocenter | C32×C7 | C2×Q8 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #92691 | C2 | direct (N × H) |
| 21. C2×C32×C7 | Q8 | semidirect |
| 38. C32×C7 | C2×Q8 | semidirect |
| 47. C2×C3×C7 | Dic6 | semidirect |
| 48. C2×C3×C7 | Dic6 | semidirect |
| 69. C3×C7 | C2×Dic6 | semidirect |
| 70. C3×C7 | C2×Dic6 | semidirect |
| 71. C2×C32 | Dic14 | semidirect |
| 74. C2×C7 | #627 | semidirect |
| 86. C32 | C2×Dic14 | semidirect |
| 91. C7 | C2×#627 | semidirect |
| 94. C2×C3 | #4248 | semidirect |
| 95. C2×C3 | Dic42 | semidirect |
| 103. C3 | C2×#4248 | semidirect |
| 104. C3 | C2×Dic42 | semidirect |
| 105. C2 | #92691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊Dic21 | 2 |
| C2×C3×Dic21 | 2 |
| C2×C3×C7×Dic3 | 2 |
| #92691 | 2 |
| C2×Dic42 | 3 |
| C2×#4248 | 3 |
| C2×#627 | 7 |