Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 107 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×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×#66627 | C2 | semidirect |
| 4. #10620649 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 11. #66728 | C4 | semidirect |
| 20. C2×C7×C4⋊C4 | D3 | semidirect |
| 36. D84 | C2×C4 | semidirect |
| 39. Dic42 | C2×C4 | semidirect |
| 54. C2×C3×C4⋊C4 | D7 | semidirect |
| 106. C2×C4⋊C4 | D21 | semidirect |
| 137. C3×C7 | #417 | semidirect |
| 183. C7 | #4966 | semidirect |
| 201. C3 | #89738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66728 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C2×#66627 | 2 |
| #10620649 | 2 |
| #10620648 | 2 |
| #89738 | 3 |
| #4966 | 7 |