Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
404 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 102 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. D3×C7×C4⋊C4 | C2 | semidirect |
| 3. C2×D3×C7⋊C8 | C2 | semidirect |
| 4. #10620648 | C2 | semidirect |
| 5. C3×#6383 | C2 | semidirect |
| 6. #10620504 | C2 | semidirect |
| 7. #10620499 | C2 | semidirect |
| 16. D3×D28 | C4 | semidirect |
| 17. C3×C7×C4⋊C4 | C22 | semidirect |
| 18. C2×C3⋊(C7⋊C8) | C22 | semidirect |
| 19. C7×C4⋊Dic3 | C22 | semidirect |
| 21. C2×C3×C7⋊C8 | C22 | semidirect |
| 29. #6383 | D3 | direct (N × H) |
| 40. D84 | C2×C4 | semidirect |
| 47. C3×D28 | C2×C4 | semidirect |
| 61. C7×C4⋊C4 | C2×D3 | semidirect |
| 64. C2×C7⋊C8 | C2×D3 | semidirect |
| 67. D3×C4⋊C4 | D7 | semidirect |
| 106. D28 | C4×D3 | semidirect |
| 118. C3×C4⋊C4 | C2×D7 | semidirect |
| 119. C4⋊Dic3 | C2×D7 | semidirect |
| 128. D3×C7 | #102 | semidirect |
| 172. C3×C7 | C2×#102 | semidirect |
| 186. C4⋊C4 | D3×D7 | semidirect |
| 229. C7 | D3×#102 | semidirect |
| 235. D3 | #6383 | direct (N × H) |
| 252. C3 | C2×#6383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D28 | 2 |
| D3×C7×C4⋊C4 | 2 |
| C2×D3×C7⋊C8 | 2 |
| #10620648 | 2 |
| C3×#6383 | 2 |
| #10620504 | 2 |
| #10620499 | 2 |
| C2×#6383 | 3 |
| D3×#102 | 7 |