Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
146 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 2. #10620795 | C2 | semidirect |
| 3. #90510 | C3 | semidirect |
| 10. #6511 | C2×C3 | semidirect |
| 107. C7 | #568⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#41⋊C3 | 2 |
| #10620795 | 2 |
| #90510 | 3 |
| C3×#1136 | 4 |
| #568⋊C3 | 7 |