Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
660 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 660 conjugacy classes of subgroups — too many to draw. Only its 262 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. C3×C7×#95 | C2 | semidirect |
| 3. C3×C7⋊#95 | C2 | semidirect |
| 4. D7×#95 | C3 | direct (N × H) |
| 9. C2×C3×C4×D7 | C4 | semidirect |
| 11. C7×#95 | C2×C3 | semidirect |
| 12. C7⋊#95 | C2×C3 | semidirect |
| 19. C2×C3×C4×C7 | C2×C4 | semidirect |
| 21. C2×C3×Dic7 | C2×C4 | semidirect |
| 27. C2×C4×D7 | C3×C4 | semidirect |
| 30. C3×#95 | D7 | direct (N × H) |
| 45. C2×C4×C7 | C2×C3×C4 | semidirect |
| 47. C2×Dic7 | C2×C3×C4 | semidirect |
| 57. C3×D7 | #95 | direct (N × H) |
| 60. #95 | C3×D7 | direct (N × H) |
| 77. C2×C3×C4 | C4×D7 | semidirect |
| 78. C3×C7 | C2×#95 | semidirect |
| 87. D7 | C3×#95 | direct (N × H) |
| 104. C2×C4 | C3×C4×D7 | semidirect |
| 105. C7 | C2×C3×#95 | semidirect |
| 118. C3 | D7×#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×D7 | 2 |
| C3×C7×#95 | 2 |
| C3×C7⋊#95 | 2 |
| D7×#95 | 3 |
| C2×C3×#95 | 7 |