Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 3. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 4. #10620523 | C2 | semidirect |
| 5. #10620504 | C2 | semidirect |
| 18. C22⋊(C7⋊C8) | D3 | semidirect |
| 43. C2×C4⋊Dic3 | D7 | semidirect |
| 111. C3×C7 | #480 | semidirect |
| 148. C7 | #4736 | semidirect |
| 165. C3 | #89739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621413 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620523 | 2 |
| #10620504 | 2 |
| #89739 | 3 |
| #4736 | 7 |