Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
154 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 29 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. C4×C7×SL(2,𝔽3) | C2 | semidirect |
| 3. C7⋊#859 | C2 | semidirect |
| 6. C7⋊GL(2,𝔽3) | C4 | semidirect |
| 8. C4×C7×Q8 | D3 | semidirect |
| 19. C7×SL(2,𝔽3) | C2×C4 | semidirect |
| 32. C4×SL(2,𝔽3) | D7 | semidirect |
| 61. C4×Q8 | D21 | semidirect |
| 79. SL(2,𝔽3) | C4×D7 | semidirect |
| 114. C7 | #5394 | semidirect |
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 |
| C4×C7×SL(2,𝔽3) | 2 |
| C7⋊#859 | 2 |
| #89798 | 3 |
| #66631 | 4 |
| #5394 | 7 |