Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
172 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 19. #5065 | C7 | direct (N × H) |
| 77. C3×C7 | #499 | semidirect |
| 99. C7 | #5065 | direct (N × H) |
| 108. C3 | C7×#499 | 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×#870 | 2 |
| C7×#808 | 2 |
| C7×#807 | 2 |
| C4×C7×C3⋊C8 | 2 |
| C7×#499 | 3 |
| #5065 | 7 |