Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 70 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×D7×D12 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. C2×C7×#213 | C2 | semidirect |
| 4. C3×#6501 | C2 | semidirect |
| 5. #10620503 | C2 | semidirect |
| 6. #10620501 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 10. C2×C3×C7×D4 | C22 | semidirect |
| 19. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 21. C2×C7×C3⋊C8 | C22 | semidirect |
| 23. C3×C4⋊Dic7 | C22 | semidirect |
| 26. #6501 | D3 | semidirect |
| 43. D84 | D4 | semidirect |
| 45. C7×D12 | D4 | semidirect |
| 56. C2×C7×D4 | C2×D3 | semidirect |
| 67. C4⋊Dic7 | C2×D3 | semidirect |
| 72. C2×#213 | D7 | semidirect |
| 88. C2×C3×D7 | D8 | semidirect |
| 119. C2×C3×D4 | C2×D7 | semidirect |
| 131. C2×C3⋊C8 | C2×D7 | semidirect |
| 159. C2×D7 | #213 | semidirect |
| 183. D12 | C22⋊D7 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 194. C2×D4 | D3×D7 | semidirect |
| 249. C7 | #5036 | semidirect |
| 275. C3 | #89928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D7×D12 | 2 |
| C2×#66632 | 2 |
| C2×C7×#213 | 2 |
| C3×#6501 | 2 |
| #10620503 | 2 |
| #10620501 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89928 | 3 |
| #5036 | 7 |