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. C3×#6458 | C2 | semidirect |
| 3. C2×#66561 | C2 | semidirect |
| 4. C2×#66560 | C2 | semidirect |
| 5. #10620648 | C2 | semidirect |
| 6. C7×#809 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 13. C2×C3×D28 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 20. C2×C7×C3⋊C8 | C22 | semidirect |
| 27. #6458 | D3 | semidirect |
| 42. D84 | D4 | semidirect |
| 44. C7×D12 | D4 | semidirect |
| 61. C2×D28 | C2×D3 | semidirect |
| 64. C7×C4⋊C4 | C2×D3 | semidirect |
| 75. #809 | D7 | semidirect |
| 88. C2×C3×D7 | D8 | semidirect |
| 126. C3×C4⋊C4 | C2×D7 | semidirect |
| 131. C2×C3⋊C8 | C2×D7 | semidirect |
| 159. C2×D7 | #213 | semidirect |
| 183. D12 | D28 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 200. C4⋊C4 | D3×D7 | semidirect |
| 249. C7 | #5036 | semidirect |
| 275. C3 | #89545 | 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×#6458 | 2 |
| C2×#66561 | 2 |
| C2×#66560 | 2 |
| #10620648 | 2 |
| C7×#809 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89545 | 3 |
| #5036 | 7 |