Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
684 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 254 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. C23×C3×C4×C7 | C2 | semidirect |
| 3. C2×C3×C22⋊Dic7 | C2 | semidirect |
| 4. C3×#6492 | C2 | direct (N × H) |
| 5. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C2×C3×Dic7⋊C4 | C2 | semidirect |
| 7. C2×#6492 | C3 | direct (N × H) |
| 12. C22×C3×C4×C7 | C22 | semidirect |
| 17. C3×C22⋊Dic7 | C22 | semidirect |
| 18. C3×(C2×D7)⋊C4 | C22 | semidirect |
| 19. C3×Dic7⋊C4 | C22 | semidirect |
| 20. C23×C4×C7 | C2×C3 | semidirect |
| 22. C2×C22⋊Dic7 | C2×C3 | semidirect |
| 23. #6492 | C2×C3 | direct (N × H) |
| 24. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 25. C2×Dic7⋊C4 | C2×C3 | semidirect |
| 46. C22×C4×C7 | C22×C3 | semidirect |
| 51. C22⋊Dic7 | C22×C3 | semidirect |
| 52. (C2×D7)⋊C4 | C22×C3 | semidirect |
| 53. Dic7⋊C4 | C22×C3 | semidirect |
| 55. C23×C3×C4 | D7 | semidirect |
| 96. C22×C3×C4 | C2×D7 | semidirect |
| 101. C2×C3×C7 | #123 | semidirect |
| 106. C23×C4 | C3×D7 | semidirect |
| 138. C3×C7 | C2×#123 | semidirect |
| 147. C22×C4 | C2×C3×D7 | semidirect |
| 152. C2×C7 | C3×#123 | semidirect |
| 183. C7 | C2×C3×#123 | semidirect |
| 186. C2×C3 | #6492 | direct (N × H) |
| 201. C3 | C2×#6492 | direct (N × H) |
| 204. C2 | C3×#6492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4×C7 | 2 |
| C22×C3×C22⋊D7 | 2 |
| C2×C3×C22⋊Dic7 | 2 |
| C3×#6492 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C2×C3×Dic7⋊C4 | 2 |
| C2×#6492 | 3 |
| C2×C3×#123 | 7 |