Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 90 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×#214 | C2 | semidirect |
| 3. C2×C7×#204 | C2 | semidirect |
| 4. C7×#897 | C2 | semidirect |
| 5. C3×C7×#102 | C2 | semidirect |
| 6. C7×(C2×D3)⋊C8 | C2 | semidirect |
| 7. C7×#809 | C2 | semidirect |
| 16. C2×C7×Dic6 | C22 | semidirect |
| 17. C2×C3×C7×C8 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 22. C2×C7×C3⋊C8 | C22 | semidirect |
| 29. C7×#102 | D3 | semidirect |
| 31. #4776 | C7 | direct (N × H) |
| 64. C2×C7×C8 | C2×D3 | semidirect |
| 66. C7×C4⋊C4 | C2×D3 | semidirect |
| 69. C2×#214 | C2×C7 | semidirect |
| 70. C2×#204 | C2×C7 | semidirect |
| 71. #897 | C2×C7 | semidirect |
| 72. C3×#102 | C2×C7 | semidirect |
| 73. (C2×D3)⋊C8 | C2×C7 | semidirect |
| 74. #809 | C2×C7 | semidirect |
| 85. C2×D3×C7 | SD16 | semidirect |
| 120. C2×Dic6 | C22×C7 | semidirect |
| 121. C2×C3×C8 | C22×C7 | semidirect |
| 122. C3×C4⋊C4 | C22×C7 | semidirect |
| 126. C2×C3⋊C8 | C22×C7 | semidirect |
| 139. #102 | D3×C7 | semidirect |
| 178. C3×C7 | #450 | semidirect |
| 190. C2×C8 | C2×D3×C7 | semidirect |
| 192. C4⋊C4 | C2×D3×C7 | semidirect |
| 210. C2×D3 | C7×SD16 | semidirect |
| 237. C7 | #4776 | direct (N × H) |
| 260. C3 | C7×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C7×D4 | 2 |
| C2×C7×#214 | 2 |
| C2×C7×#204 | 2 |
| C7×#897 | 2 |
| C3×C7×#102 | 2 |
| C7×(C2×D3)⋊C8 | 2 |
| C7×#809 | 2 |
| C7×#450 | 3 |
| #4776 | 7 |