Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10621409 | C2 | semidirect |
| 3. C2×C7×#208 | C2 | semidirect |
| 4. #10620500 | C2 | semidirect |
| 10. C2×C3×D28 | C4 | semidirect |
| 13. C4⋊Dic21 | C22 | semidirect |
| 16. C2×C7×C3⋊C8 | C22 | semidirect |
| 39. C2×D28 | Dic3 | semidirect |
| 48. C2×#208 | D7 | semidirect |
| 84. C2×C3⋊C8 | C2×D7 | semidirect |
| 116. C3×C7 | #418 | semidirect |
| 155. C7 | #5215 | semidirect |
| 170. C3 | #89903 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| #10621409 | 2 |
| C2×C7×#208 | 2 |
| #10620500 | 2 |
| #89903 | 3 |
| #5215 | 7 |