Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
220 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 17. C3×#1144 | C4 | semidirect |
| 48. #1144 | Dic3 | direct (N × H) |
| 69. C7×Dic3 | Q16 | semidirect |
| 128. C3×C7 | C4×Q16 | semidirect |
| 152. Dic3 | #1144 | direct (N × H) |
| 166. C7 | Dic3×Q16 | semidirect |
| 179. C3 | C4×#1144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×Dic3 | 2 |
| C2×C3×#1144 | 2 |
| Dic3×Dic14 | 2 |
| #10620674 | 2 |
| #10620523 | 2 |
| #10620505 | 2 |
| Dic3×C7⋊C8 | 2 |
| C4×#1144 | 3 |
| Dic3×Q16 | 7 |