Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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×D4×D21 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. C2×D168 | C2 | semidirect |
| 4. #10621378 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. #10620659 | C2 | semidirect |
| 7. #10620648 | C2 | semidirect |
| 16. C2×D84 | C22 | semidirect |
| 18. C2×C3×C7×C8 | C22 | semidirect |
| 19. C3×C7×C4⋊C4 | C22 | semidirect |
| 22. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 28. C7×#102 | D3 | semidirect |
| 40. C3×C7×D4 | D4 | semidirect |
| 49. D84 | D4 | semidirect |
| 63. C2×C7×C8 | C2×D3 | semidirect |
| 64. C7×C4⋊C4 | C2×D3 | semidirect |
| 73. C3×#102 | D7 | semidirect |
| 89. C2×D21 | D8 | semidirect |
| 103. C7×D4 | D12 | semidirect |
| 126. C2×C3×C8 | C2×D7 | semidirect |
| 127. C3×C4⋊C4 | C2×D7 | semidirect |
| 144. #102 | D21 | semidirect |
| 172. C3×D4 | D28 | semidirect |
| 186. C3×C7 | #447 | semidirect |
| 199. C2×C8 | C2×D21 | semidirect |
| 200. C4⋊C4 | C2×D21 | semidirect |
| 241. D4 | D84 | 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×D4×D21 | 2 |
| C2×#66632 | 2 |
| C2×D168 | 2 |
| #10621378 | 2 |
| C3×C7×#102 | 2 |
| #10620659 | 2 |
| #10620648 | 2 |
| #89545 | 3 |
| #4773 | 7 |