Finite Group DatabasebetaFinite Group DatabasebetaOrder 1008.
176 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C7 | C2×D32 |
| commutator, cosocle | C2×C32 | C23×C7 |
| Frattini | C2 | C2×D32×C7 |
| Fitting | C22×C32×C7 | C22 |
| socle | C2×C32×C7 | C23 |
| hypercenter | C22×C7 | D32 |
| hypocenter | C32 | C7×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C7 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×C3⋊Dic3 | C2 | semidirect |
| 2. C3×C7×#67 | C2 | semidirect |
| 3. C7×#627 | C2 | semidirect |
| 4. C7×#625 | C2 | semidirect |
| 5. D3×C7×Dic3 | C2 | semidirect |
| 14. C7×#67 | D3 | semidirect |
| 20. #3805 | C7 | direct (N × H) |
| 35. C2×C3⋊Dic3 | C2×C7 | semidirect |
| 36. C3×#67 | C2×C7 | semidirect |
| 37. #627 | C2×C7 | semidirect |
| 38. #625 | C2×C7 | semidirect |
| 39. D3×Dic3 | C2×C7 | semidirect |
| 40. C32×C7 | #41 | semidirect |
| 65. #67 | D3×C7 | semidirect |
| 72. C3×C7 | #237 | semidirect |
| 90. C32 | C7×#41 | semidirect |
| 96. C7 | #3805 | direct (N × H) |
| 109. C3 | C7×#237 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×C3⋊Dic3 | 2 |
| C3×C7×#67 | 2 |
| C7×#627 | 2 |
| C7×#625 | 2 |
| D3×C7×Dic3 | 2 |
| C7×#237 | 3 |
| #3805 | 7 |