Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 108 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×D3×C7⋊C8 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. (C2×D3)⋊(C7⋊C8) | C2 | semidirect |
| 7. Dic3×C7⋊C8 | C2 | semidirect |
| 24. C22×C7⋊C8 | D3 | semidirect |
| 36. C7×#67 | C8 | semidirect |
| 45. C3×C7⋊C8 | D4 | semidirect |
| 68. C22×C3×C7 | C2×C8 | semidirect |
| 72. C2×D3×C7 | C2×C8 | semidirect |
| 78. C7×Dic3 | C2×C8 | semidirect |
| 95. C7⋊C8 | #67 | direct (N × H) |
| 126. C22×C7 | D3×C8 | semidirect |
| 140. #67 | C7⋊C8 | direct (N × H) |
| 150. C3×C7 | C8×D4 | semidirect |
| 171. C22×C3 | C2×C7⋊C8 | semidirect |
| 175. C2×D3 | C2×C7⋊C8 | semidirect |
| 181. Dic3 | C2×C7⋊C8 | semidirect |
| 198. C7 | C8×#67 | semidirect |
| 209. C22 | D3×C7⋊C8 | semidirect |
| 217. C3 | D4×C7⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#67 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620669 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| (C2×D3)⋊(C7⋊C8) | 2 |
| Dic3×C7⋊C8 | 2 |
| D4×C7⋊C8 | 3 |
| C8×#67 | 7 |