Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
288 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 86 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×#127 | C2 | semidirect |
| 2. C2×C7×#214 | C2 | semidirect |
| 3. C2×C7×#213 | C2 | semidirect |
| 4. C7×#875 | C2 | semidirect |
| 5. C7×#803 | C2 | semidirect |
| 18. C7×#127 | D3 | semidirect |
| 21. #5074 | C7 | direct (N × H) |
| 32. C7×C3⋊C8 | D4 | semidirect |
| 42. C3×#127 | C2×C7 | semidirect |
| 43. C2×#214 | C2×C7 | semidirect |
| 44. C2×#213 | C2×C7 | semidirect |
| 45. #875 | C2×C7 | semidirect |
| 46. #803 | C2×C7 | semidirect |
| 82. #127 | D3×C7 | semidirect |
| 103. C3⋊C8 | C7×D4 | semidirect |
| 104. C3×C7 | #496 | semidirect |
| 137. C7 | #5074 | direct (N × H) |
| 150. C3 | C7×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×C7×#214 | 2 |
| C2×C7×#213 | 2 |
| C7×#875 | 2 |
| C7×#803 | 2 |
| C7×#496 | 3 |
| #5074 | 7 |