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 |
|---|---|---|
| 1. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 4. C7×C3⋊#95 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 15. C2×C7×C4⋊C4 | D3 | semidirect |
| 20. #4992 | C7 | direct (N × H) |
| 45. C2×C3×C4⋊C4 | C2×C7 | semidirect |
| 48. C3⋊#95 | C2×C7 | semidirect |
| 49. C3⋊#95 | C2×C7 | semidirect |
| 95. C2×C4⋊C4 | D3×C7 | semidirect |
| 130. C3×C7 | #397 | semidirect |
| 175. C7 | #4992 | direct (N × H) |
| 196. C3 | C7×#397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#397 | 3 |
| #4992 | 7 |