Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 3. C4×Dic42 | C2 | semidirect |
| 5. #10620649 | C2 | semidirect |
| 6. #10620646 | C2 | semidirect |
| 7. #10620642 | C2 | semidirect |
| 15. #66633 | C4 | semidirect |
| 40. Dic42 | C2×C4 | semidirect |
| 42. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 178. C7 | #5018 | semidirect |
| 194. C3 | #89790 | 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 |
| C2×#66633 | 2 |
| C4×Dic42 | 2 |
| #10620671 | 2 |
| #10620649 | 2 |
| #10620646 | 2 |
| #10620642 | 2 |
| #89790 | 3 |
| #5018 | 7 |