Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
376 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 94 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. C3×C7×C22⋊Q8 | C2 | semidirect |
| 3. C2×C3×#1143 | C2 | semidirect |
| 4. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 5. C3×#6383 | C2 | semidirect |
| 6. #89818 | C3 | direct (N × H) |
| 8. C2×C3×C7×Q8 | C22 | semidirect |
| 14. C3×C7×C4⋊C4 | C22 | semidirect |
| 17. C2×C3×C7⋊C8 | C22 | semidirect |
| 19. C7×C22⋊Q8 | C2×C3 | semidirect |
| 20. C2×#1143 | C2×C3 | semidirect |
| 21. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 22. #6383 | C2×C3 | semidirect |
| 40. C2×C7×Q8 | C22×C3 | semidirect |
| 46. C7×C4⋊C4 | C22×C3 | semidirect |
| 49. C2×C7⋊C8 | C22×C3 | semidirect |
| 52. C3×C22⋊Q8 | D7 | semidirect |
| 57. C22×C3×C7 | SD16 | semidirect |
| 84. C2×C3×Q8 | C2×D7 | semidirect |
| 92. C3×C4⋊C4 | C2×D7 | semidirect |
| 101. C22⋊Q8 | C3×D7 | semidirect |
| 106. C22×C7 | C3×SD16 | semidirect |
| 131. C3×C7 | #450 | semidirect |
| 133. C2×Q8 | C2×C3×D7 | semidirect |
| 141. C4⋊C4 | C2×C3×D7 | semidirect |
| 154. C22×C3 | #1143 | semidirect |
| 175. C7 | C3×#450 | semidirect |
| 187. C22 | C3×#1143 | semidirect |
| 193. C3 | #89818 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D28 | 2 |
| C3×C7×C22⋊Q8 | 2 |
| C2×C3×#1143 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| C3×#6383 | 2 |
| #89818 | 3 |
| C3×#450 | 7 |