Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
224 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 224 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. C2×C7×#216 | C2 | semidirect |
| 3. Dic6×Dic7 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. Dic7⋊(C3⋊C8) | C2 | semidirect |
| 59. C2×#216 | D7 | semidirect |
| 142. C3×C7 | #464 | semidirect |
| 186. C7 | #5054 | semidirect |
| 202. C3 | #89957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#216 | 2 |
| C3×#6510 | 2 |
| Dic6×Dic7 | 2 |
| C2×#66563 | 2 |
| #10620674 | 2 |
| Dic7⋊(C3⋊C8) | 2 |
| #10620500 | 2 |
| #89957 | 3 |
| #5054 | 7 |