Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 92 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×C7×C3⋊C8 | C2 | semidirect |
| 3. C2×D21⋊C8 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. #10620518 | C2 | semidirect |
| 6. #10620492 | C2 | semidirect |
| 7. #10620486 | C2 | semidirect |
| 25. C22⋊(C7⋊C8) | D3 | semidirect |
| 36. #4268 | C8 | semidirect |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C22×C3⋊C8 | D7 | semidirect |
| 68. C22×C3×C7 | C2×C8 | semidirect |
| 72. C2×D21 | C2×C8 | semidirect |
| 78. Dic21 | C2×C8 | semidirect |
| 123. C22×C7 | D3×C8 | semidirect |
| 149. C3⋊C8 | C22⋊D7 | semidirect |
| 150. C3×C7 | C8×D4 | semidirect |
| 171. C22×C3 | C8×D7 | semidirect |
| 198. C7 | #67⋊C8 | semidirect |
| 209. C22 | D21⋊C8 | semidirect |
| 217. C3 | C8×C22⋊D7 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#4268 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×D21⋊C8 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| #10620518 | 2 |
| #10620492 | 2 |
| #10620486 | 2 |
| C8×C22⋊D7 | 3 |
| #67⋊C8 | 7 |