Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 102 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. C2×C7×#208 | C2 | semidirect |
| 3. C2×D3×C7×C8 | C2 | semidirect |
| 4. C3×C7×C22⋊C8 | C2 | semidirect |
| 5. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 6. C7×#815 | C2 | semidirect |
| 7. C7×Dic3⋊C8 | C2 | semidirect |
| 27. C7×C22⋊C8 | D3 | semidirect |
| 29. #4728 | C7 | direct (N × H) |
| 45. C7×C3⋊C8 | D4 | semidirect |
| 60. C2×#208 | C2×C7 | semidirect |
| 61. C2×D3×C8 | C2×C7 | semidirect |
| 62. C3×C22⋊C8 | C2×C7 | semidirect |
| 63. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 64. #815 | C2×C7 | semidirect |
| 65. Dic3⋊C8 | C2×C7 | semidirect |
| 72. C2×D3×C7 | M16 | semidirect |
| 119. C22⋊C8 | D3×C7 | semidirect |
| 149. C3⋊C8 | C7×D4 | semidirect |
| 150. C3×C7 | #435 | semidirect |
| 175. C2×D3 | C7×M16 | semidirect |
| 198. C7 | #4728 | direct (N × H) |
| 217. C3 | C7×#435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C7×#67 | 2 |
| C2×C7×#208 | 2 |
| C2×D3×C7×C8 | 2 |
| C3×C7×C22⋊C8 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#815 | 2 |
| C7×Dic3⋊C8 | 2 |
| C7×#435 | 3 |
| #4728 | 7 |