Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 19. #4985 | C7 | direct (N × H) |
| 109. C3×C7 | #400 | semidirect |
| 145. C7 | #4985 | direct (N × H) |
| 161. C3 | C7×#400 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C7×Dic3⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#400 | 3 |
| #4985 | 7 |