Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C3×#6396 | C2 | direct (N × H) |
| 5. C2×#6396 | C3 | direct (N × H) |
| 19. #6396 | C2×C3 | direct (N × H) |
| 76. C2×C3×C7 | #108 | semidirect |
| 100. C3×C7 | C2×#108 | semidirect |
| 113. C2×C7 | C3×#108 | semidirect |
| 133. C7 | C2×C3×#108 | semidirect |
| 136. C2×C3 | #6396 | direct (N × H) |
| 146. C3 | C2×#6396 | direct (N × H) |
| 149. C2 | C3×#6396 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C2×C3×#1136 | 2 |
| C22×C3×C7⋊C8 | 2 |
| C3×#6396 | 2 |
| C2×#6396 | 3 |
| C2×C3×#108 | 7 |