Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 142 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×C7×#208 | C2 | semidirect |
| 3. C22×C7×C3⋊C8 | C2 | semidirect |
| 4. C7×#830 | C2 | semidirect |
| 21. #5234 | C7 | direct (N × H) |
| 48. C2×#208 | C2×C7 | semidirect |
| 49. C22×C3⋊C8 | C2×C7 | semidirect |
| 50. #830 | C2×C7 | semidirect |
| 117. C3×C7 | #408 | semidirect |
| 156. C7 | #5234 | direct (N × H) |
| 170. C3 | C7×#408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C2×C7×#208 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C7×#830 | 2 |
| C7×#408 | 3 |
| #5234 | 7 |