Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
380 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 86 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. C3×#6455 | C2 | semidirect |
| 3. C2×#66557 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 6. #10620503 | C2 | semidirect |
| 7. #10620501 | C2 | semidirect |
| 15. D7×D12 | C4 | semidirect |
| 16. C3×C7×C4⋊C4 | C22 | semidirect |
| 17. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 18. C2×C7×C3⋊C8 | C22 | semidirect |
| 20. C3×C4⋊Dic7 | C22 | semidirect |
| 25. #6455 | D3 | semidirect |
| 58. C7×C4⋊C4 | C2×D3 | semidirect |
| 60. C4⋊Dic7 | C2×D3 | semidirect |
| 70. #809 | D7 | semidirect |
| 115. C3×C4⋊C4 | C2×D7 | semidirect |
| 120. C2×C3⋊C8 | C2×D7 | semidirect |
| 169. C3×C7 | #418 | semidirect |
| 181. C4⋊C4 | D3×D7 | semidirect |
| 225. C7 | #5001 | semidirect |
| 248. C3 | #89542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D12 | 2 |
| C3×#6455 | 2 |
| C2×#66557 | 2 |
| #10620648 | 2 |
| C7×#809 | 2 |
| #10620503 | 2 |
| #10620501 | 2 |
| #89542 | 3 |
| #5001 | 7 |