Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 222 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×C3×C7×Q16 | C2 | semidirect |
| 3. C2×C7×#216 | C2 | semidirect |
| 4. D3×C7×Q16 | C2 | direct (N × H) |
| 5. C2×C7×Dic12 | C2 | semidirect |
| 15. C3×C7×Q16 | C22 | semidirect |
| 17. C7×#216 | C22 | semidirect |
| 19. C7×Dic12 | C22 | semidirect |
| 25. C2×C7×Q16 | D3 | direct (N × H) |
| 27. C2×D3×Q16 | C7 | direct (N × H) |
| 52. C7×Q16 | C2×D3 | direct (N × H) |
| 57. C2×C3×Q16 | C2×C7 | semidirect |
| 58. C2×#216 | C2×C7 | semidirect |
| 59. D3×Q16 | C2×C7 | direct (N × H) |
| 60. C2×Dic12 | C2×C7 | semidirect |
| 63. C2×D3×C7 | Q16 | direct (N × H) |
| 93. C3×Q16 | C22×C7 | semidirect |
| 95. #216 | C22×C7 | semidirect |
| 97. Dic12 | C22×C7 | semidirect |
| 99. C2×C3×C7 | C2×Q16 | semidirect |
| 101. D3×C7 | C2×Q16 | direct (N × H) |
| 106. C2×Q16 | D3×C7 | direct (N × H) |
| 131. C3×C7 | C22×Q16 | semidirect |
| 141. Q16 | C2×D3×C7 | direct (N × H) |
| 146. C2×C7 | D3×Q16 | direct (N × H) |
| 149. C2×D3 | C7×Q16 | direct (N × H) |
| 171. C7 | C2×D3×Q16 | direct (N × H) |
| 172. C2×C3 | C2×C7×Q16 | semidirect |
| 174. D3 | C2×C7×Q16 | direct (N × H) |
| 183. C3 | C22×C7×Q16 | semidirect |
| 185. C2 | D3×C7×Q16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×Q8 | 2 |
| C2×C3×C7×Q16 | 2 |
| C2×C7×#216 | 2 |
| D3×C7×Q16 | 2 |
| C2×C7×Dic12 | 2 |
| C2×D3×C7×C8 | 2 |
| C22×C7×Q16 | 3 |
| C2×D3×Q16 | 7 |