Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10621091 | C2 | semidirect |
| 3. #10620673 | C2 | semidirect |
| 4. C3×#6408 | C2 | semidirect |
| 5. #10620531 | C2 | semidirect |
| 8. C2×C7×#67 | C4 | semidirect |
| 10. C22×C7×Dic3 | C4 | semidirect |
| 14. C2×C4×D3×C7 | C4 | semidirect |
| 15. C2×C7×Dic6 | C4 | semidirect |
| 24. #6408 | D3 | semidirect |
| 98. C2×#67 | Dic7 | semidirect |
| 100. C22×Dic3 | Dic7 | semidirect |
| 104. C2×C4×D3 | Dic7 | semidirect |
| 105. C2×Dic6 | Dic7 | semidirect |
| 153. C3×C7 | #410 | semidirect |
| 205. C7 | #4740 | semidirect |
| 225. C3 | #90012 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#237 | 2 |
| #10621091 | 2 |
| #10620673 | 2 |
| C3×#6408 | 2 |
| #10620531 | 2 |
| #90012 | 3 |
| #4740 | 7 |