Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
516 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 192 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×ΓL(1,𝔽8)⋊Q8 | C2 | semidirect |
| 3. #6514⋊C3 | C2 | direct (N × H) |
| 4. C2×#1144⋊C3 | C2 | semidirect |
| 5. C2×#1142⋊C3 | C2 | semidirect |
| 6. C2×#1136⋊C3 | C2 | semidirect |
| 7. C2×#6514 | C3 | semidirect |
| 19. C2×ΓL(1,𝔽8)⋊Q8 | C22 | semidirect |
| 20. #1144⋊C3 | C22 | semidirect |
| 21. #1142⋊C3 | C22 | semidirect |
| 22. #1136⋊C3 | C22 | semidirect |
| 25. C22×Dic14 | C2×C3 | semidirect |
| 26. #6514 | C2×C3 | semidirect |
| 27. C2×#1144 | C2×C3 | semidirect |
| 28. C2×#1142 | C2×C3 | semidirect |
| 29. C2×#1136 | C2×C3 | semidirect |
| 61. C2×Dic14 | C22×C3 | semidirect |
| 62. #1144 | C22×C3 | semidirect |
| 63. #1142 | C22×C3 | semidirect |
| 64. #1136 | C22×C3 | semidirect |
| 120. C2×ΓL(1,𝔽8) | #137 | semidirect |
| 157. ΓL(1,𝔽8) | C2×#137 | semidirect |
| 176. C2×C7 | C3×#137 | semidirect |
| 207. C7 | C2×C3×#137 | semidirect |
| 225. C2 | #6514⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×ΓL(1,𝔽8) | 2 |
| C22×ΓL(1,𝔽8)⋊Q8 | 2 |
| #6514⋊C3 | 2 |
| C2×#1144⋊C3 | 2 |
| C2×#1142⋊C3 | 2 |
| C2×#1136⋊C3 | 2 |
| C2×#6514 | 3 |
| C2×C3×#137 | 7 |