Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 1. C3×C7×C4⋊Q8 | C2 | semidirect |
| 3. C3×#6384 | C2 | semidirect |
| 5. C3×#6377 | C2 | semidirect |
| 6. #89861 | C3 | direct (N × H) |
| 16. C7×C4⋊Q8 | C2×C3 | semidirect |
| 18. #6384 | C2×C3 | semidirect |
| 20. #6377 | C2×C3 | semidirect |
| 41. C3×C4⋊Q8 | D7 | semidirect |
| 79. C4⋊Q8 | C3×D7 | semidirect |
| 103. C3×C7 | #489 | semidirect |
| 136. C7 | C3×#489 | semidirect |
| 150. C3 | #89861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×C4⋊Q8 | 2 |
| C3×#6438 | 2 |
| C3×#6384 | 2 |
| C3×#6383 | 2 |
| C3×#6377 | 2 |
| #89861 | 3 |
| C3×#489 | 7 |