Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C7×#830 | C2 | semidirect |
| 4. C7×#809 | C2 | semidirect |
| 5. C7×#807 | C2 | semidirect |
| 17. C2×C7×C4⋊C4 | D3 | semidirect |
| 21. #4967 | C7 | direct (N × H) |
| 42. C2×C3×C4⋊C4 | C2×C7 | semidirect |
| 44. #830 | C2×C7 | semidirect |
| 45. #809 | C2×C7 | semidirect |
| 46. #807 | C2×C7 | semidirect |
| 85. C2×C4⋊C4 | D3×C7 | semidirect |
| 111. C3×C7 | #480 | semidirect |
| 148. C7 | #4967 | direct (N × H) |
| 165. C3 | C7×#480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C7×#930 | 2 |
| C7×#830 | 2 |
| C7×#809 | 2 |
| C7×#807 | 2 |
| C7×#480 | 3 |
| #4967 | 7 |