Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
340 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. C3×C7×#95 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 6. #89446 | C3 | direct (N × H) |
| 17. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 18. C7×#95 | C2×C3 | semidirect |
| 19. C7⋊#95 | C2×C3 | semidirect |
| 49. C3×#95 | D7 | semidirect |
| 99. #95 | C3×D7 | semidirect |
| 130. C3×C7 | #397 | semidirect |
| 175. C7 | C3×#397 | semidirect |
| 196. C3 | #89446 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×(C2×D7)⋊C4 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C3×C7×#95 | 2 |
| C3×C7⋊#95 | 2 |
| #89446 | 3 |
| C3×#397 | 7 |