Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10620938 | C2 | semidirect |
| 5. C7×#816 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. #10620510 | C2 | semidirect |
| 27. Dic7⋊C8 | D3 | semidirect |
| 65. #816 | D7 | semidirect |
| 74. C3×Dic7 | SD16 | semidirect |
| 128. Dic7 | #204 | semidirect |
| 145. C3×C7 | #461 | semidirect |
| 190. C7 | #4841 | semidirect |
| 206. C3 | #89590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66623 | 2 |
| #10620980 | 2 |
| #10620938 | 2 |
| C2×#66568 | 2 |
| C7×#816 | 2 |
| C3×Dic7⋊C8 | 2 |
| #10620510 | 2 |
| #89590 | 3 |
| #4841 | 7 |