Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
236 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 112 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. #10620523 | C2 | semidirect |
| 5. #10620520 | C2 | semidirect |
| 15. C3×#1136 | C4 | semidirect |
| 32. C3×C7⋊C8 | C2×C4 | semidirect |
| 41. #1136 | Dic3 | semidirect |
| 68. C7⋊C8 | C2×Dic3 | semidirect |
| 108. C3×C7 | #428 | semidirect |
| 143. C7 | #5121 | semidirect |
| 158. C3 | #89767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊Dic21 | 2 |
| C7×#926 | 2 |
| C2×C3×#1136 | 2 |
| #10620523 | 2 |
| #10620520 | 2 |
| #89767 | 3 |
| #5121 | 7 |