Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
146 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 30 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×C7×#226 | C2 | semidirect |
| 3. C4×C7×SL(2,𝔽3) | C2 | semidirect |
| 12. C4×C7×Q8 | D3 | semidirect |
| 16. #5395 | C7 | direct (N × H) |
| 35. C2×#226 | C2×C7 | semidirect |
| 36. C4×SL(2,𝔽3) | C2×C7 | semidirect |
| 68. C4×Q8 | D3×C7 | semidirect |
| 122. C7 | #5395 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×GL(2,𝔽3) | 2 |
| C2×C7×#226 | 2 |
| C4×C7×SL(2,𝔽3) | 2 |
| C7×#464 | 3 |
| C7×(C2×D3)⋊C4 | 4 |
| #5395 | 7 |