Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
336 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10621662 | C2 | semidirect |
| 2. C7×#949 | C2 | semidirect |
| 3. #10621013 | C2 | semidirect |
| 4. #10620866 | C2 | semidirect |
| 5. C3×#6411 | C2 | semidirect |
| 6. #10620516 | C2 | semidirect |
| 7. #10620495 | C2 | semidirect |
| 17. C2×C7×D12 | C22 | semidirect |
| 21. C7×#208 | C22 | semidirect |
| 22. C3×C4×Dic7 | C22 | semidirect |
| 23. C3×#1136 | C22 | semidirect |
| 30. #6411 | D3 | semidirect |
| 37. C3×C7×Q8 | D4 | semidirect |
| 39. C3×C7×D4 | D4 | semidirect |
| 47. D84 | D4 | semidirect |
| 50. Dic42 | D4 | semidirect |
| 72. C4×Dic7 | C2×D3 | semidirect |
| 73. #1136 | C2×D3 | semidirect |
| 75. #949 | D7 | semidirect |
| 98. C7×Q8 | D12 | semidirect |
| 102. C7×D4 | D12 | semidirect |
| 127. C2×D12 | C2×D7 | semidirect |
| 132. #208 | C2×D7 | semidirect |
| 164. C3×Q8 | C22⋊D7 | semidirect |
| 166. C3×D4 | C22⋊D7 | semidirect |
| 184. C3×C7 | #453 | semidirect |
| 225. Q8 | #4247 | semidirect |
| 236. D4 | #4247 | semidirect |
| 244. C7 | #4822 | semidirect |
| 264. C3 | #89970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621662 | 2 |
| C7×#949 | 2 |
| #10621013 | 2 |
| #10620866 | 2 |
| C3×#6411 | 2 |
| #10620516 | 2 |
| #10620495 | 2 |
| #89970 | 3 |
| #4822 | 7 |