Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 174 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. C2×C3×C42×C7 | C2 | semidirect |
| 3. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 4. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 5. #89711 | C3 | direct (N × H) |
| 12. C2×C3×D28 | C4 | semidirect |
| 17. C2×C42×C7 | C2×C3 | semidirect |
| 18. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 19. C2×C4⋊Dic7 | C2×C3 | semidirect |
| 32. C2×C3×C4×C7 | D4 | semidirect |
| 42. C2×D28 | C3×C4 | semidirect |
| 49. C2×C3×C42 | D7 | semidirect |
| 61. C3×C4×C7 | C22⋊C4 | semidirect |
| 75. C2×C4×C7 | C3×D4 | semidirect |
| 98. C2×C42 | C3×D7 | semidirect |
| 110. C4×C7 | C3×C22⋊C4 | semidirect |
| 125. C2×C3×C4 | D28 | semidirect |
| 127. C3×C7 | #390 | semidirect |
| 156. C3×C4 | (C2×D7)⋊C4 | semidirect |
| 170. C2×C4 | C3×D28 | semidirect |
| 172. C7 | C3×#390 | semidirect |
| 191. C4 | C3×(C2×D7)⋊C4 | semidirect |
| 192. C3 | #89711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C2×C3×C42×C7 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #89711 | 3 |
| C3×#390 | 7 |