Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
252 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 120 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. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 50. C7×Dic3 | M16 | semidirect |
| 96. C3×C7 | #423 | semidirect |
| 116. Dic3 | #1136 | semidirect |
| 127. C7 | #5118 | semidirect |
| 139. C3 | #89696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66627 | 2 |
| C2×C4×C7×Dic3 | 2 |
| C2×C3×#1136 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #89696 | 3 |
| #5118 | 7 |