Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
216 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10621352 | C2 | semidirect |
| 4. #10620647 | C2 | semidirect |
| 5. C4⋊(C3⋊(C7⋊C8)) | C2 | semidirect |
| 24. C3×C7×D4 | Q8 | semidirect |
| 60. C7×D4 | Dic6 | semidirect |
| 99. C3×D4 | Dic14 | semidirect |
| 108. C3×C7 | #476 | semidirect |
| 135. D4 | Dic42 | semidirect |
| 143. C7 | #5008 | semidirect |
| 158. C3 | #89780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×D4 | 2 |
| #10621352 | 2 |
| #10620671 | 2 |
| #10620647 | 2 |
| C4⋊(C3⋊(C7⋊C8)) | 2 |
| #89780 | 3 |
| #5008 | 7 |