Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 160 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 |
|---|---|---|
| 1. C22×Dic42 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. C2×#66570 | C2 | semidirect |
| 5. #10620875 | C2 | direct (N × H) |
| 6. C2×#66565 | C2 | semidirect |
| 13. C2×Dic42 | C22 | semidirect |
| 20. C7×#208 | C22 | semidirect |
| 22. #66570 | C22 | semidirect |
| 23. #66565 | C22 | semidirect |
| 71. C2×#208 | D7 | semidirect |
| 116. #208 | C2×D7 | semidirect |
| 119. C2×C3×C7 | #137 | semidirect |
| 157. C3×C7 | C2×#137 | semidirect |
| 175. C2×C7 | #951 | semidirect |
| 207. C7 | C2×#951 | semidirect |
| 210. C2×C3 | #6472 | semidirect |
| 222. C3 | C2×#6472 | semidirect |
| 225. C2 | #10620875 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic42 | 2 |
| C2×C3×#1157 | 2 |
| C2×C7×#208 | 2 |
| C2×#66570 | 2 |
| #10620875 | 2 |
| C2×#66565 | 2 |
| C2×#6472 | 3 |
| C2×#951 | 7 |