Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 3. C2×#66569 | C2 | semidirect |
| 5. #10620646 | C2 | semidirect |
| 6. C3×#6384 | C2 | semidirect |
| 7. #10620508 | C2 | semidirect |
| 27. #6384 | D3 | semidirect |
| 68. C2×D3×C7 | Q16 | semidirect |
| 142. C3×C7 | #467 | semidirect |
| 163. C2×D3 | #1144 | semidirect |
| 186. C7 | #4813 | semidirect |
| 202. C3 | #89823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#897 | 2 |
| #10620931 | 2 |
| C2×#66569 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620646 | 2 |
| C3×#6384 | 2 |
| #10620508 | 2 |
| #89823 | 3 |
| #4813 | 7 |