Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 68 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. #10621353 | C2 | semidirect |
| 3. C7×C4⋊(C3⋊C8) | C2 | semidirect |
| 4. #10620525 | C2 | semidirect |
| 5. #10620522 | C2 | semidirect |
| 57. C4⋊(C3⋊C8) | D7 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | #5009 | semidirect |
| 182. C3 | #89619 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10621353 | 2 |
| C3×C4×D28 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| #10620525 | 2 |
| #10620522 | 2 |
| #10620500 | 2 |
| #89619 | 3 |
| #5009 | 7 |