Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
162 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 31 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. C7⋊#859 | C2 | semidirect |
| 3. C7×#859 | C2 | semidirect |
| 6. D7×SL(2,𝔽3) | C4 | semidirect |
| 22. Q8×D7 | Dic3 | semidirect |
| 34. #859 | D7 | semidirect |
| 118. C7 | #5420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×SL(2,𝔽3) | 2 |
| C7⋊#859 | 2 |
| C7×#859 | 2 |
| #89574 | 3 |
| (C2×D7)⋊Dic3 | 4 |
| #5420 | 7 |