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 |
|---|---|---|
| 6. #89836 | C3 | direct (N × H) |
| 77. C3×C7 | #499 | semidirect |
| 99. C7 | C3×#499 | semidirect |
| 108. C3 | #89836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#125 | 2 |
| C3×#6433 | 2 |
| C3×#6382 | 2 |
| C3×#6381 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89836 | 3 |
| C3×#499 | 7 |