Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
372 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊Dic21 | C2 | semidirect |
| 3. C2×Dic7⋊Dic3 | C2 | semidirect |
| 5. C3×C7⋊#95 | C2 | semidirect |
| 20. C7⋊#95 | D3 | semidirect |
| 133. C3×C7 | #399 | semidirect |
| 179. C7 | #4677 | semidirect |
| 200. C3 | #89721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic21 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| C3×C7⋊#95 | 2 |
| #89721 | 3 |
| #4677 | 7 |