Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
204 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C3×#6453 | C2 | semidirect |
| 5. C3×#6392 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. C3×#6382 | C2 | semidirect |
| 8. #89538 | C3 | direct (N × H) |
| 21. #6453 | C2×C3 | semidirect |
| 24. #6392 | C2×C3 | semidirect |
| 25. Dic7⋊C8 | C2×C3 | semidirect |
| 26. #6382 | C2×C3 | semidirect |
| 127. C3×C7 | #478 | semidirect |
| 166. C7 | C3×#478 | semidirect |
| 182. C3 | #89538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×Dic7 | 2 |
| C3×#6453 | 2 |
| C3×C7×#102 | 2 |
| C3×#6406 | 2 |
| C3×#6392 | 2 |
| C3×Dic7⋊C8 | 2 |
| C3×#6382 | 2 |
| #89538 | 3 |
| C3×#478 | 7 |