Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×#6458 | C2 | semidirect |
| 2. #10621011 | C2 | semidirect |
| 3. C2×#66560 | C2 | semidirect |
| 4. C2×D7×C3⋊C8 | C2 | semidirect |
| 5. #10620646 | C2 | semidirect |
| 6. C7×#809 | C2 | semidirect |
| 7. #10620500 | C2 | semidirect |
| 25. #6458 | D3 | semidirect |
| 45. C3⋊(C7⋊C8) | D4 | semidirect |
| 65. #809 | D7 | semidirect |
| 76. C2×C3×D7 | D8 | semidirect |
| 135. C2×D7 | #213 | semidirect |
| 158. C3×C7 | #466 | semidirect |
| 210. C7 | #5038 | semidirect |
| 232. C3 | #89547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6458 | 2 |
| #10621011 | 2 |
| C2×#66560 | 2 |
| C2×D7×C3⋊C8 | 2 |
| #10620646 | 2 |
| C7×#809 | 2 |
| #10620500 | 2 |
| #89547 | 3 |
| #5038 | 7 |