Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 59 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. #10621387 | C2 | semidirect |
| 2. C2×C3×C7×C16 | C2 | semidirect |
| 3. Dic168 | C2 | semidirect |
| 4. #10620639 | C2 | semidirect |
| 5. D336 | C2 | semidirect |
| 15. C2×C7×C16 | D3 | semidirect |
| 35. C2×C3×C16 | D7 | semidirect |
| 66. C2×C16 | D21 | semidirect |
| 79. C3×C7 | #508 | semidirect |
| 102. C7 | #4904 | semidirect |
| 111. C3 | #89676 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621387 | 2 |
| C2×C3×C7×C16 | 2 |
| Dic168 | 2 |
| #10620639 | 2 |
| D336 | 2 |
| #89676 | 3 |
| #4904 | 7 |