Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 84 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. Dic3×Dic14 | C2 | semidirect |
| 4. #10620657 | C2 | semidirect |
| 5. C7×#815 | C2 | semidirect |
| 6. #10620506 | C2 | semidirect |
| 17. C3×#1132 | C4 | semidirect |
| 39. C3×Dic14 | C2×C4 | semidirect |
| 41. C3×C7×C8 | C2×C4 | semidirect |
| 54. #1132 | Dic3 | semidirect |
| 61. #815 | D7 | semidirect |
| 85. Dic14 | C2×Dic3 | semidirect |
| 87. C7×C8 | C2×Dic3 | semidirect |
| 134. C3×C8 | C4×D7 | semidirect |
| 136. C3×C7 | #440 | semidirect |
| 177. C8 | Dic3×D7 | semidirect |
| 178. C7 | #5164 | semidirect |
| 194. C3 | #89482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1132 | 2 |
| Dic3×D28 | 2 |
| Dic3×Dic14 | 2 |
| #10620657 | 2 |
| C7×#815 | 2 |
| #10620506 | 2 |
| #10620500 | 2 |
| #89482 | 3 |
| #5164 | 7 |