Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 83 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. C3×C7×#106 | C2 | semidirect |
| 4. #10620656 | C2 | semidirect |
| 5. #10620646 | C2 | semidirect |
| 14. C8×D21 | C4 | semidirect |
| 17. C7×#106 | D3 | semidirect |
| 40. C3×#106 | D7 | semidirect |
| 76. #106 | D21 | semidirect |
| 94. C3×C7 | #427 | semidirect |
| 123. C7 | #4860 | semidirect |
| 135. C3 | #89632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| #10621375 | 2 |
| C3×C7×#106 | 2 |
| #10620656 | 2 |
| #10620646 | 2 |
| #89632 | 3 |
| #4860 | 7 |