Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 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×#6499 | C2 | semidirect |
| 3. C2×C3×#1132 | C2 | semidirect |
| 4. C3×#6456 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C3×Dic7⋊C8 | C2 | semidirect |
| 7. C3×#6384 | C2 | semidirect |
| 8. #89559 | C3 | direct (N × H) |
| 22. #6499 | C2×C3 | semidirect |
| 24. C2×#1132 | C2×C3 | semidirect |
| 25. #6456 | C2×C3 | semidirect |
| 26. C7×#102 | C2×C3 | semidirect |
| 27. Dic7⋊C8 | C2×C3 | semidirect |
| 28. #6384 | C2×C3 | semidirect |
| 65. C3×#102 | D7 | semidirect |
| 120. #102 | C3×D7 | semidirect |
| 150. C3×C7 | #463 | semidirect |
| 198. C7 | C3×#463 | semidirect |
| 217. C3 | #89559 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#6499 | 2 |
| C2×C3×#1141 | 2 |
| C2×C3×#1132 | 2 |
| C3×#6456 | 2 |
| C3×C7×#102 | 2 |
| C3×Dic7⋊C8 | 2 |
| C3×#6384 | 2 |
| #89559 | 3 |
| C3×#463 | 7 |