Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
208 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 1. #10621392 | C2 | semidirect |
| 3. C2×#66623 | C2 | semidirect |
| 4. #10621384 | C2 | semidirect |
| 5. C3×C7×#108 | C2 | semidirect |
| 6. #10620663 | C2 | semidirect |
| 7. #10620662 | C2 | semidirect |
| 28. C7×#108 | D3 | semidirect |
| 67. C3×#108 | D7 | semidirect |
| 118. #108 | D21 | semidirect |
| 145. C3×C7 | #471 | semidirect |
| 189. C7 | #4898 | semidirect |
| 202. C3 | #89670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621392 | 2 |
| #10621391 | 2 |
| C2×#66623 | 2 |
| #10621384 | 2 |
| C3×C7×#108 | 2 |
| #10620663 | 2 |
| #10620662 | 2 |
| #89670 | 3 |
| #4898 | 7 |