Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
132 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 62 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×#6392 | C2 | semidirect |
| 3. C2×C3×C7⋊C16 | C2 | semidirect |
| 4. #89357 | C3 | direct (N × H) |
| 7. C3×C7×D8 | C4 | semidirect |
| 12. #6392 | C2×C3 | semidirect |
| 13. C2×C7⋊C16 | C2×C3 | semidirect |
| 24. C7×D8 | C3×C4 | semidirect |
| 48. C3×D8 | Dic7 | semidirect |
| 73. C3×C7 | #357 | semidirect |
| 76. D8 | C3×Dic7 | semidirect |
| 98. C7 | C3×#357 | semidirect |
| 110. C3 | #89357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×D8 | 2 |
| C3×#6392 | 2 |
| C2×C3×C7⋊C16 | 2 |
| #89357 | 3 |
| C3×#357 | 7 |