Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
288 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 83 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×D168 | C2 | semidirect |
| 2. C2×#66623 | C2 | semidirect |
| 3. #10621358 | C2 | semidirect |
| 4. #10621357 | C2 | semidirect |
| 5. C3×C7×#97 | C2 | semidirect |
| 20. C7×#97 | D3 | semidirect |
| 32. C3×C7×C8 | D4 | semidirect |
| 46. C3×#97 | D7 | semidirect |
| 66. C7×C8 | D12 | semidirect |
| 84. #97 | D21 | semidirect |
| 103. C3×C8 | D28 | semidirect |
| 104. C3×C7 | #496 | semidirect |
| 136. C8 | D84 | semidirect |
| 137. C7 | #4712 | semidirect |
| 150. C3 | #89484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D168 | 2 |
| C2×#66623 | 2 |
| #10621358 | 2 |
| #10621357 | 2 |
| C3×C7×#97 | 2 |
| #89484 | 3 |
| #4712 | 7 |