Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 4. #10620648 | C2 | direct (N × H) |
| 11. C2×D84 | C4 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 16. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 18. C2×C7×C4⋊C4 | D3 | semidirect |
| 35. D84 | C2×C4 | semidirect |
| 45. C7×C4⋊C4 | C2×D3 | semidirect |
| 49. C2×C3×C4⋊C4 | D7 | semidirect |
| 88. C3×C4⋊C4 | C2×D7 | semidirect |
| 91. C2×C3×C7 | #102 | semidirect |
| 98. C2×C4⋊C4 | D21 | semidirect |
| 127. C3×C7 | C2×#102 | semidirect |
| 138. C4⋊C4 | C2×D21 | semidirect |
| 139. C2×C7 | #809 | semidirect |
| 171. C7 | C2×#809 | semidirect |
| 172. C2×C3 | #6383 | semidirect |
| 189. C3 | C2×#6383 | semidirect |
| 191. C2 | #10620648 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C2×C3×C7×C4⋊C4 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| #10620648 | 2 |
| C2×#6383 | 3 |
| C2×#809 | 7 |