Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 110 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. C3×C4×Dic14 | C2 | semidirect |
| 4. C3×C4×C7×C8 | C2 | semidirect |
| 6. C3×#6391 | C2 | semidirect |
| 7. C3×#6390 | C2 | semidirect |
| 8. C4×#1132 | C3 | direct (N × H) |
| 20. C3×#1132 | C4 | direct (N × H) |
| 23. C4×Dic14 | C2×C3 | semidirect |
| 24. C4×C7×C8 | C2×C3 | semidirect |
| 26. #6391 | C2×C3 | semidirect |
| 27. #6390 | C2×C3 | semidirect |
| 40. C3×Dic14 | C2×C4 | semidirect |
| 42. C3×C7×C8 | C2×C4 | semidirect |
| 54. #1132 | C3×C4 | direct (N × H) |
| 61. C3×C4×C8 | D7 | semidirect |
| 67. C3×C4×C7 | SD16 | semidirect |
| 85. Dic14 | C2×C3×C4 | semidirect |
| 87. C7×C8 | C2×C3×C4 | semidirect |
| 110. C4×C8 | C3×D7 | semidirect |
| 116. C4×C7 | C3×SD16 | semidirect |
| 135. C3×C8 | C4×D7 | semidirect |
| 136. C3×C7 | C4×SD16 | semidirect |
| 161. C3×C4 | #1132 | direct (N × H) |
| 177. C8 | C3×C4×D7 | semidirect |
| 178. C7 | C3×C4×SD16 | semidirect |
| 191. C4 | C3×#1132 | direct (N × H) |
| 194. C3 | C4×#1132 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1132 | 2 |
| C3×C4×D28 | 2 |
| C3×C4×Dic14 | 2 |
| C3×C4×C7×C8 | 2 |
| C3×#6395 | 2 |
| C3×#6391 | 2 |
| C3×#6390 | 2 |
| C4×#1132 | 3 |
| C3×C4×SD16 | 7 |