Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C22×C3×Dic14 | C2 | semidirect |
| 3. C2×#66564 | C2 | semidirect |
| 4. #10620669 | C2 | semidirect |
| 5. #10620505 | C2 | semidirect |
| 18. C22×Dic14 | D3 | semidirect |
| 36. C3×Dic14 | D4 | semidirect |
| 56. C22×C3×C7 | SD16 | semidirect |
| 78. Dic14 | #67 | semidirect |
| 106. C22×C7 | #215 | semidirect |
| 126. C3×C7 | #448 | semidirect |
| 145. C22×C3 | #1142 | semidirect |
| 168. C7 | #5227 | semidirect |
| 179. C22 | #66564 | semidirect |
| 185. C3 | #89812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic14 | 2 |
| C7×#930 | 2 |
| C2×#66564 | 2 |
| #10620669 | 2 |
| #10620505 | 2 |
| #89812 | 3 |
| #5227 | 7 |