Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
228 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C2×C3×C7×C4⋊C4 | C2 | semidirect |
| 3. C3×C22⋊(C7⋊C8) | C2 | semidirect |
| 4. C3×#6383 | C2 | semidirect |
| 5. C3×#6381 | C2 | semidirect |
| 6. #89739 | C3 | direct (N × H) |
| 16. C2×C7×C4⋊C4 | C2×C3 | semidirect |
| 18. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 19. #6383 | C2×C3 | semidirect |
| 20. #6381 | C2×C3 | semidirect |
| 43. C2×C3×C4⋊C4 | D7 | semidirect |
| 85. C2×C4⋊C4 | C3×D7 | semidirect |
| 111. C3×C7 | #480 | semidirect |
| 148. C7 | C3×#480 | semidirect |
| 165. C3 | #89739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×C4⋊C4 | 2 |
| C3×#6493 | 2 |
| C3×C22⋊(C7⋊C8) | 2 |
| C3×#6383 | 2 |
| C3×#6381 | 2 |
| #89739 | 3 |
| C3×#480 | 7 |