Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 68 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×#66681 | C2 | semidirect |
| 2. #10621378 | C2 | semidirect |
| 3. C2×#66562 | C2 | semidirect |
| 4. C2×#66561 | C2 | semidirect |
| 5. C7×#809 | C2 | semidirect |
| 6. C3×#6383 | C2 | semidirect |
| 7. #10620492 | C2 | semidirect |
| 11. C2×D84 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 20. C2×C7×C3⋊C8 | C22 | semidirect |
| 21. C2×C3×C7⋊C8 | C22 | semidirect |
| 30. #6383 | D3 | semidirect |
| 48. C7×D12 | D4 | semidirect |
| 50. C3×D28 | D4 | semidirect |
| 64. C7×C4⋊C4 | C2×D3 | semidirect |
| 67. C2×C7⋊C8 | C2×D3 | semidirect |
| 75. #809 | D7 | semidirect |
| 82. C2×D21 | D8 | semidirect |
| 112. D28 | D12 | semidirect |
| 127. C3×C4⋊C4 | C2×D7 | semidirect |
| 130. C2×C3⋊C8 | C2×D7 | semidirect |
| 181. D12 | D28 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 200. C4⋊C4 | D3×D7 | semidirect |
| 249. C7 | #4773 | 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×#66681 | 2 |
| #10621378 | 2 |
| C2×#66562 | 2 |
| C2×#66561 | 2 |
| C7×#809 | 2 |
| C3×#6383 | 2 |
| #10620492 | 2 |
| #89545 | 3 |
| #4773 | 7 |