Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
644 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 192 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×C7×Dic6 | C2 | semidirect |
| 3. C2×#66629 | C2 | semidirect |
| 5. C2×Dic3⋊Dic7 | C2 | semidirect |
| 6. C2×Dic7⋊Dic3 | C2 | semidirect |
| 8. #10620983 | C2 | direct (N × H) |
| 17. C2×C7×Dic6 | C22 | semidirect |
| 21. #66629 | C22 | semidirect |
| 23. Dic3⋊Dic7 | C22 | semidirect |
| 24. Dic7⋊Dic3 | C22 | semidirect |
| 38. C22×C3×D7 | Q8 | semidirect |
| 71. C22×Dic6 | D7 | semidirect |
| 85. C2×C3×D7 | C2×Q8 | semidirect |
| 96. C22×D7 | Dic6 | semidirect |
| 122. C2×Dic6 | C2×D7 | semidirect |
| 128. C2×C3×C7 | C22⋊Q8 | semidirect |
| 148. C2×D7 | C2×Dic6 | semidirect |
| 174. C3×C7 | C2×C22⋊Q8 | semidirect |
| 191. C2×C7 | #878 | semidirect |
| 229. C7 | C2×#878 | semidirect |
| 231. C2×C3 | #6509 | semidirect |
| 249. C3 | C2×#6509 | semidirect |
| 251. C2 | #10620983 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C22×Dic3×D7 | 2 |
| C2×#66629 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×(C2×D7)⋊Dic3 | 2 |
| #10620983 | 2 |
| C2×#6509 | 3 |
| C2×#878 | 7 |