Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
| 17. C7×#108 | D3 | semidirect |
| 40. C3×#108 | D7 | semidirect |
| 74. #108 | D21 | semidirect |
| 90. C3×C7 | #430 | semidirect |
| 117. C7 | #4893 | semidirect |
| 127. C3 | #89665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M16×D21 | 2 |
| C2×#66622 | 2 |
| C3×C7×#108 | 2 |
| #10620661 | 2 |
| #10620658 | 2 |
| #89665 | 3 |
| #4893 | 7 |