Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
168 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 44 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. #10621395 | C2 | semidirect |
| 2. #10620839 | C2 | semidirect |
| 3. C7×#827 | C2 | semidirect |
| 4. C3×#6400 | C2 | semidirect |
| 5. #10620483 | C2 | semidirect |
| 6. #10620477 | C2 | semidirect |
| 7. D21⋊C16 | C2 | semidirect |
| 24. #6400 | D3 | semidirect |
| 54. #827 | D7 | semidirect |
| 116. C3×C7 | #508 | semidirect |
| 150. C7 | #4912 | semidirect |
| 162. C3 | #89688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621395 | 2 |
| #10620839 | 2 |
| C7×#827 | 2 |
| C3×#6400 | 2 |
| #10620483 | 2 |
| #10620477 | 2 |
| D21⋊C16 | 2 |
| #89688 | 3 |
| #4912 | 7 |