Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 8. C4×#1144 | C3 | direct (N × H) |
| 15. C3×#1144 | C4 | direct (N × H) |
| 48. #1144 | C3×C4 | direct (N × H) |
| 65. C3×C4×C7 | Q16 | semidirect |
| 110. C4×C7 | C3×Q16 | semidirect |
| 128. C3×C7 | C4×Q16 | semidirect |
| 150. C3×C4 | #1144 | direct (N × H) |
| 166. C7 | C3×C4×Q16 | semidirect |
| 176. C4 | C3×#1144 | direct (N × H) |
| 179. C3 | C4×#1144 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C2×C3×#1144 | 2 |
| C3×C4×Dic14 | 2 |
| C3×#6409 | 2 |
| C3×#6384 | 2 |
| C3×#6381 | 2 |
| C3×C4×C7⋊C8 | 2 |
| C4×#1144 | 3 |
| C3×C4×Q16 | 7 |