Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
244 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 72. C3×Dic7 | Q16 | semidirect |
| 120. Dic7 | #216 | semidirect |
| 137. C3×C7 | #494 | semidirect |
| 177. C7 | #5092 | semidirect |
| 188. C3 | #89953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66635 | 2 |
| C2×C7×#216 | 2 |
| C3×#6507 | 2 |
| #10620938 | 2 |
| C2×#66570 | 2 |
| C2×#66569 | 2 |
| C3⋊C8×Dic7 | 2 |
| #89953 | 3 |
| #5092 | 7 |