Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 144 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. C22×C3⋊(C7⋊C8) | C2 | semidirect |
| 3. C2×C7×C4⋊Dic3 | C2 | semidirect |
| 4. #10620499 | C2 | direct (N × H) |
| 11. C2×C3×D28 | C4 | semidirect |
| 14. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 16. C7×C4⋊Dic3 | C22 | semidirect |
| 35. C3×D28 | C2×C4 | semidirect |
| 42. C2×D28 | Dic3 | semidirect |
| 49. C2×C4⋊Dic3 | D7 | semidirect |
| 78. D28 | C2×Dic3 | semidirect |
| 88. C4⋊Dic3 | C2×D7 | semidirect |
| 91. C2×C3×C7 | #102 | semidirect |
| 127. C3×C7 | C2×#102 | semidirect |
| 139. C2×C7 | #832 | semidirect |
| 171. C7 | C2×#832 | semidirect |
| 173. C2×C3 | #6383 | semidirect |
| 189. C3 | C2×#6383 | semidirect |
| 191. C2 | #10620499 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C22×C3⋊(C7⋊C8) | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| #10620499 | 2 |
| C2×#6383 | 3 |
| C2×#832 | 7 |