Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 4. #10620646 | C2 | semidirect |
| 5. C7×#807 | C2 | semidirect |
| 6. #10620522 | C2 | semidirect |
| 7. #10620521 | C2 | semidirect |
| 20. #66557 | C4 | semidirect |
| 39. C3⋊(C7⋊C8) | C2×C4 | semidirect |
| 40. C7×C3⋊C8 | C2×C4 | semidirect |
| 59. #807 | D7 | semidirect |
| 129. C3⋊C8 | C4×D7 | semidirect |
| 130. C3×C7 | #428 | semidirect |
| 170. C7 | #4995 | semidirect |
| 186. C3 | #89653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6455 | 2 |
| D7×C4⋊Dic3 | 2 |
| C2×#66557 | 2 |
| #10620646 | 2 |
| C7×#807 | 2 |
| #10620522 | 2 |
| #10620521 | 2 |
| #89653 | 3 |
| #4995 | 7 |