Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 27. #4791 | C7 | direct (N × H) |
| 29. C3×C7×Q8 | Q8 | semidirect |
| 70. C7×Q8 | Dic6 | semidirect |
| 111. C3×Q8 | C7×Q8 | semidirect |
| 122. C3×C7 | #475 | semidirect |
| 148. Q8 | C7×Dic6 | semidirect |
| 158. C7 | #4791 | direct (N × H) |
| 171. C3 | C7×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×Dic3 | 2 |
| C7×#888 | 2 |
| C3×C7×#103 | 2 |
| C7×#835 | 2 |
| C7×#817 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#808 | 2 |
| C7×#475 | 3 |
| #4791 | 7 |