Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 64 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. C3×#6453 | C2 | semidirect |
| 3. #10620647 | C2 | semidirect |
| 5. #10620525 | C2 | semidirect |
| 6. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 21. #6453 | D3 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | #5066 | semidirect |
| 182. C3 | #89538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6453 | 2 |
| D12×Dic7 | 2 |
| #10620647 | 2 |
| C7×#809 | 2 |
| #10620525 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620501 | 2 |
| #89538 | 3 |
| #5066 | 7 |