Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
396 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 78 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. C7×#1004 | C2 | semidirect |
| 2. C7×#937 | C2 | semidirect |
| 3. C7×#882 | C2 | semidirect |
| 4. C3×C7×#99 | C2 | semidirect |
| 5. C7×#806 | C2 | semidirect |
| 7. C23×D3×C7 | C22 | semidirect |
| 16. C3×C7×C22⋊C4 | C22 | semidirect |
| 17. C7×#217 | C22 | semidirect |
| 24. C7×#99 | D3 | semidirect |
| 25. #4741 | C7 | direct (N × H) |
| 26. C23×C3×C7 | D4 | semidirect |
| 32. C22×D3×C7 | D4 | semidirect |
| 35. C2×C3×C4×C7 | D4 | semidirect |
| 42. C2×C7×Dic3 | D4 | semidirect |
| 59. C7×C22⋊C4 | C2×D3 | semidirect |
| 60. #1004 | C2×C7 | semidirect |
| 61. #937 | C2×C7 | semidirect |
| 62. #882 | C2×C7 | semidirect |
| 63. C3×#99 | C2×C7 | semidirect |
| 64. #806 | C2×C7 | semidirect |
| 88. C23×C7 | D12 | semidirect |
| 103. C2×C4×C7 | D12 | semidirect |
| 104. C23×D3 | C22×C7 | semidirect |
| 113. C3×C22⋊C4 | C22×C7 | semidirect |
| 114. #217 | C22×C7 | semidirect |
| 127. #99 | D3×C7 | semidirect |
| 145. C23×C3 | C7×D4 | semidirect |
| 151. C22×D3 | C7×D4 | semidirect |
| 154. C2×C3×C4 | C7×D4 | semidirect |
| 161. C2×Dic3 | C7×D4 | semidirect |
| 166. C3×C7 | B(4,𝔽2) | semidirect |
| 179. C22⋊C4 | C2×D3×C7 | semidirect |
| 208. C23 | C7×D12 | semidirect |
| 223. C2×C4 | C7×D12 | semidirect |
| 224. C7 | #4741 | direct (N × H) |
| 248. C3 | C7×B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#1004 | 2 |
| C7×#937 | 2 |
| C7×#882 | 2 |
| C3×C7×#99 | 2 |
| C7×#806 | 2 |
| C7×B(4,𝔽2) | 3 |
| #4741 | 7 |