Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. #5064 | C7 | direct (N × H) |
| 29. C7×C3⋊C8 | Q8 | semidirect |
| 91. C3⋊C8 | C7×Q8 | semidirect |
| 92. C3×C7 | #501 | semidirect |
| 120. C7 | #5064 | direct (N × H) |
| 131. C3 | C7×#501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#125 | 2 |
| C7×#869 | 2 |
| C7×#808 | 2 |
| C7×#807 | 2 |
| C7×#803 | 2 |
| C7×#501 | 3 |
| #5064 | 7 |