Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 91 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×C8×D21 | C2 | semidirect |
| 3. C4⋊C4×D21 | C2 | semidirect |
| 4. C3×C7×#102 | C2 | semidirect |
| 5. #10620671 | C2 | semidirect |
| 6. #10620660 | C2 | semidirect |
| 7. #10620648 | C2 | semidirect |
| 13. D4×D21 | C4 | semidirect |
| 17. C2×C3×C7×C8 | C22 | semidirect |
| 18. C3×C7×C4⋊C4 | C22 | semidirect |
| 19. C4⋊Dic21 | C22 | semidirect |
| 21. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 26. C7×#102 | D3 | semidirect |
| 38. C3×C7×D4 | C2×C4 | semidirect |
| 45. D84 | C2×C4 | semidirect |
| 59. C2×C7×C8 | C2×D3 | semidirect |
| 60. C7×C4⋊C4 | C2×D3 | semidirect |
| 68. C3×#102 | D7 | semidirect |
| 96. C7×D4 | C4×D3 | semidirect |
| 117. C2×C3×C8 | C2×D7 | semidirect |
| 118. C3×C4⋊C4 | C2×D7 | semidirect |
| 128. D21 | #102 | direct (N × H) |
| 135. #102 | D21 | direct (N × H) |
| 159. C3×D4 | C4×D7 | semidirect |
| 172. C3×C7 | C2×#102 | semidirect |
| 183. C2×C8 | C2×D21 | semidirect |
| 186. C4⋊C4 | C2×D21 | semidirect |
| 219. D4 | C4×D21 | semidirect |
| 229. C7 | D3×#102 | semidirect |
| 252. C3 | D7×#102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D21 | 2 |
| C2×C8×D21 | 2 |
| C4⋊C4×D21 | 2 |
| C3×C7×#102 | 2 |
| #10620671 | 2 |
| #10620660 | 2 |
| #10620648 | 2 |
| D7×#102 | 3 |
| D3×#102 | 7 |