Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
180 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 52 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. C7×C3⋊#95 | C2 | semidirect |
| 3. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 7. C2×D84 | C4 | semidirect |
| 10. C4⋊Dic21 | C4 | semidirect |
| 14. C22⋊(C7⋊C8) | D3 | semidirect |
| 38. C3⋊#95 | D7 | semidirect |
| 106. C3×C7 | #327 | semidirect |
| 145. C7 | #4470 | semidirect |
| 164. C3 | #89246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621413 | 2 |
| C7×C3⋊#95 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #89246 | 3 |
| #4470 | 7 |