Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
212 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 77 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×C7×#108 | C2 | semidirect |
| 4. #10620661 | C2 | semidirect |
| 5. #10620658 | C2 | semidirect |
| 18. C7×#108 | D3 | semidirect |
| 44. C3×#108 | D7 | semidirect |
| 79. D21 | #108 | direct (N × H) |
| 84. #108 | D21 | direct (N × H) |
| 104. C3×C7 | C2×#108 | semidirect |
| 137. C7 | D3×#108 | semidirect |
| 150. C3 | D7×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×D21 | 2 |
| C2×C8×D21 | 2 |
| C3×C7×#108 | 2 |
| #10620661 | 2 |
| #10620658 | 2 |
| D7×#108 | 3 |
| D3×#108 | 7 |