Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 21. #5020 | C7 | direct (N × H) |
| 23. C3×C7×Q8 | Q8 | semidirect |
| 57. C7×Q8 | Dic6 | semidirect |
| 91. C3×Q8 | C7×Q8 | semidirect |
| 100. C3×C7 | #475 | semidirect |
| 123. Q8 | C7×Dic6 | semidirect |
| 131. C7 | #5020 | direct (N × H) |
| 143. C3 | C7×#475 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C7×#869 | 2 |
| C7×#835 | 2 |
| C7×#808 | 2 |
| C7×C4⋊(C3⋊C8) | 2 |
| C7×#475 | 3 |
| #5020 | 7 |