Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 122 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. C2×C7×Dic3⋊C4 | C2 | semidirect |
| 5. C7×C3⋊#95 | C2 | semidirect |
| 17. C2×C7×C4⋊C4 | D3 | semidirect |
| 21. #4993 | C7 | direct (N × H) |
| 47. C2×C3×C4⋊C4 | C2×C7 | semidirect |
| 50. C2×Dic3⋊C4 | C2×C7 | semidirect |
| 51. C3⋊#95 | C2×C7 | semidirect |
| 99. C2×C4⋊C4 | D3×C7 | semidirect |
| 133. C3×C7 | #399 | semidirect |
| 179. C7 | #4993 | direct (N × H) |
| 200. C3 | C7×#399 | 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 |
| C2×C7×Dic3⋊C4 | 2 |
| C7×C3⋊#95 | 2 |
| C7×#399 | 3 |
| #4993 | 7 |