Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 122 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. #89796 | C3 | direct (N × H) |
| 29. C3×C7⋊C8 | Q8 | semidirect |
| 59. C7⋊C8 | C3×Q8 | semidirect |
| 92. C3×C7 | #446 | semidirect |
| 120. C7 | C3×#446 | semidirect |
| 131. C3 | #89796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| C3×#6377 | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89796 | 3 |
| C3×#446 | 7 |