Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
108 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 4. #89274 | C3 | direct (N × H) |
| 20. C3×C7⋊C8 | C8 | semidirect |
| 42. C7⋊C8 | C3×C8 | semidirect |
| 67. C3×C7 | #335 | semidirect |
| 89. C7 | C3×#335 | semidirect |
| 99. C3 | #89274 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊C8 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| C3×C4×C7⋊C8 | 2 |
| #89274 | 3 |
| C3×#335 | 7 |