Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 136 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×C7×C3⋊C8 | C2 | semidirect |
| 3. C2×C3×C4⋊Dic7 | C2 | semidirect |
| 4. #10620503 | C2 | direct (N × H) |
| 10. C2×D84 | C4 | semidirect |
| 14. C2×C7×C3⋊C8 | C22 | semidirect |
| 16. C3×C4⋊Dic7 | C22 | semidirect |
| 19. C2×C4⋊Dic7 | D3 | semidirect |
| 33. D84 | C2×C4 | semidirect |
| 47. C4⋊Dic7 | C2×D3 | semidirect |
| 50. C22×C3⋊C8 | D7 | semidirect |
| 90. C2×C3⋊C8 | C2×D7 | semidirect |
| 91. C2×C3×C7 | #102 | semidirect |
| 127. C3×C7 | C2×#102 | semidirect |
| 139. C2×C7 | #809 | semidirect |
| 171. C7 | C2×#809 | semidirect |
| 172. C2×C3 | #6395 | semidirect |
| 189. C3 | C2×#6395 | semidirect |
| 191. C2 | #10620503 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D84 | 2 |
| C22×C7×C3⋊C8 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| #10620503 | 2 |
| C2×#6395 | 3 |
| C2×#809 | 7 |