Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
292 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 126 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. C7×#824 | C2 | direct (N × H) |
| 24. C2×#824 | C7 | direct (N × H) |
| 58. #824 | C2×C7 | direct (N × H) |
| 101. C2×C3×C7 | #101 | semidirect |
| 132. C3×C7 | C2×#101 | semidirect |
| 149. C2×C7 | #824 | direct (N × H) |
| 176. C7 | C2×#824 | direct (N × H) |
| 179. C2×C3 | C7×#101 | semidirect |
| 190. C3 | C2×C7×#101 | semidirect |
| 193. C2 | C7×#824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Dic6 | 2 |
| C2×C3×C7×M16 | 2 |
| C2×C7×#208 | 2 |
| C7×#824 | 2 |
| C2×C7×#101 | 3 |
| C2×#824 | 7 |