Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
340 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 112 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×C4×Dic21 | C2 | semidirect |
| 3. C2×C3×#1136 | C2 | semidirect |
| 4. #10620513 | C2 | direct (N × H) |
| 11. C7×#235 | C4 | semidirect |
| 13. C2×C7×D12 | C4 | semidirect |
| 15. C2×C7×Dic6 | C4 | semidirect |
| 17. C4×Dic21 | C22 | semidirect |
| 19. C3×#1136 | C22 | semidirect |
| 23. C2×#1136 | D3 | semidirect |
| 40. C7×D12 | C2×C4 | semidirect |
| 44. C7×Dic6 | C2×C4 | semidirect |
| 59. #1136 | C2×D3 | semidirect |
| 103. #235 | Dic7 | semidirect |
| 105. C2×D12 | Dic7 | semidirect |
| 107. C2×Dic6 | Dic7 | semidirect |
| 115. C2×C3×C7 | #104 | semidirect |
| 148. D12 | C2×Dic7 | semidirect |
| 152. Dic6 | C2×Dic7 | semidirect |
| 154. C3×C7 | C2×#104 | semidirect |
| 173. C2×C7 | #825 | semidirect |
| 207. C7 | C2×#825 | semidirect |
| 210. C2×C3 | #6411 | semidirect |
| 225. C3 | C2×#6411 | semidirect |
| 229. C2 | #10620513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#235 | 2 |
| C2×C4×Dic21 | 2 |
| C2×C3×#1136 | 2 |
| #10620513 | 2 |
| C2×#6411 | 3 |
| C2×#825 | 7 |