Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
188 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 39. C3⋊(C7⋊C8) | Q8 | semidirect |
| 122. C3×C7 | #446 | semidirect |
| 158. C7 | #4828 | semidirect |
| 171. C3 | #89600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic42 | 2 |
| C3×C7×C4⋊C8 | 2 |
| #10620654 | 2 |
| #10620653 | 2 |
| C8×Dic21 | 2 |
| #10620642 | 2 |
| #89600 | 3 |
| #4828 | 7 |