Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
400 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 230 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 |
|---|---|---|
| 6. #90261 | C3 | direct (N × H) |
| 22. C3×C7×Q8 | Q8 | semidirect |
| 50. C7×Q8 | C3×Q8 | semidirect |
| 81. C3×Q8 | Dic14 | semidirect |
| 87. C3×C7 | #557 | semidirect |
| 107. Q8 | C3×Dic14 | semidirect |
| 113. C7 | C3×#557 | semidirect |
| 123. C3 | #90261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×C7×Q8 | 2 |
| C3×Q8×Dic7 | 2 |
| C3×#6453 | 2 |
| C3×#6432 | 2 |
| C3×C4×Dic14 | 2 |
| #90261 | 3 |
| C3×#557 | 7 |