Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 132 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×D3×C7⋊C8 | C2 | semidirect |
| 3. #10620669 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 15. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 16. C2×C3×C7⋊C8 | C22 | semidirect |
| 22. C22⋊(C7⋊C8) | D3 | direct (N × H) |
| 27. C22×D3×C7 | C8 | semidirect |
| 52. C2×C7⋊C8 | C2×D3 | semidirect |
| 60. C22×C3×C7 | C2×C8 | semidirect |
| 67. C2×D3×C7 | C2×C8 | semidirect |
| 108. D3×C7 | C22⋊C8 | semidirect |
| 123. C22×C7 | D3×C8 | semidirect |
| 132. C22×D3 | C7⋊C8 | semidirect |
| 147. C3×C7 | C2×C22⋊C8 | semidirect |
| 167. C22×C3 | C2×C7⋊C8 | semidirect |
| 173. C2×D3 | C2×C7⋊C8 | semidirect |
| 198. C7 | D3×C22⋊C8 | semidirect |
| 204. D3 | C22⋊(C7⋊C8) | direct (N × H) |
| 214. C22 | D3×C7⋊C8 | semidirect |
| 220. C3 | C2×C22⋊(C7⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3×C7 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620669 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| C2×C22⋊(C7⋊C8) | 3 |
| D3×C22⋊C8 | 7 |