Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
684 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 176 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. C22×Dic3×D7 | C2 | semidirect |
| 3. C2×C4⋊Dic21 | C2 | semidirect |
| 4. C2×C7×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C2×C3×(C2×D7)⋊C4 | C2 | semidirect |
| 6. C2×Dic7⋊Dic3 | C2 | semidirect |
| 7. C2×(C2×D3)⋊Dic7 | C2 | semidirect |
| 8. #10620976 | C2 | direct (N × H) |
| 20. C2×Dic3×D7 | C22 | semidirect |
| 21. C4⋊Dic21 | C22 | semidirect |
| 22. C7×(C2×D3)⋊C4 | C22 | semidirect |
| 23. C3×(C2×D7)⋊C4 | C22 | semidirect |
| 24. Dic7⋊Dic3 | C22 | semidirect |
| 25. (C2×D3)⋊Dic7 | C22 | semidirect |
| 30. C2×(C2×D7)⋊C4 | D3 | semidirect |
| 69. (C2×D7)⋊C4 | C2×D3 | semidirect |
| 76. C2×(C2×D3)⋊C4 | D7 | semidirect |
| 132. (C2×D3)⋊C4 | C2×D7 | semidirect |
| 135. C2×C3×C7 | #123 | semidirect |
| 187. C3×C7 | C2×#123 | semidirect |
| 205. C2×C7 | #886 | semidirect |
| 248. C7 | C2×#886 | semidirect |
| 250. C2×C3 | #6446 | semidirect |
| 272. C3 | C2×#6446 | semidirect |
| 275. C2 | #10620976 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4245 | 2 |
| C22×Dic3×D7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×C7×(C2×D3)⋊C4 | 2 |
| C2×C3×(C2×D7)⋊C4 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| C2×(C2×D3)⋊Dic7 | 2 |
| #10620976 | 2 |
| C2×#6446 | 3 |
| C2×#886 | 7 |