Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
476 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 126 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×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 4. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 6. #89763 | C3 | direct (N × H) |
| 18. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 19. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 20. C2×(C2×D7)⋊C4 | C2×C3 | semidirect |
| 21. C7⋊#95 | C2×C3 | semidirect |
| 37. C2×C3×C4×C7 | D4 | semidirect |
| 53. C2×C3×C4⋊C4 | D7 | semidirect |
| 88. C2×C4×C7 | C3×D4 | semidirect |
| 110. C2×C4⋊C4 | C3×D7 | semidirect |
| 147. C2×C3×C4 | D28 | semidirect |
| 149. C3×C7 | #394 | semidirect |
| 199. C2×C4 | C3×D28 | semidirect |
| 201. C7 | C3×#394 | semidirect |
| 224. C3 | #89763 | 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×C7×C4⋊C4 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C3×C7⋊#95 | 2 |
| #89763 | 3 |
| C3×#394 | 7 |