Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
240 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 240 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. C2×C3×C7×M16 | C2 | semidirect |
| 3. C7×#924 | C2 | semidirect |
| 4. C2×C7×#204 | C2 | semidirect |
| 5. C7×#821 | C2 | semidirect |
| 6. C7×#818 | C2 | semidirect |
| 7. C7×#816 | C2 | semidirect |
| 23. C2×C7×M16 | D3 | semidirect |
| 29. #5134 | C7 | direct (N × H) |
| 45. C3×C7×C8 | D4 | semidirect |
| 59. C2×C3×M16 | C2×C7 | semidirect |
| 61. #924 | C2×C7 | semidirect |
| 62. C2×#204 | C2×C7 | semidirect |
| 63. #821 | C2×C7 | semidirect |
| 64. #818 | C2×C7 | semidirect |
| 65. #816 | C2×C7 | semidirect |
| 95. C7×C8 | #67 | semidirect |
| 115. C2×M16 | D3×C7 | semidirect |
| 149. C3×C8 | C7×D4 | semidirect |
| 150. C3×C7 | #468 | semidirect |
| 197. C8 | C7×#67 | semidirect |
| 198. C7 | #5134 | direct (N × H) |
| 217. C3 | C7×#468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×M16 | 2 |
| C7×#930 | 2 |
| C7×#924 | 2 |
| C2×C7×#204 | 2 |
| C7×#821 | 2 |
| C7×#818 | 2 |
| C7×#816 | 2 |
| C7×#468 | 3 |
| #5134 | 7 |