Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
324 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 87 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. C3×C7×#127 | C2 | semidirect |
| 2. C2×#66632 | C2 | semidirect |
| 3. #10621357 | C2 | semidirect |
| 4. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 13. C7×#127 | D3 | semidirect |
| 26. C3⋊(C7⋊C8) | D4 | semidirect |
| 34. C3×#127 | D7 | semidirect |
| 43. C3×C4×C7 | D8 | semidirect |
| 68. #127 | D21 | semidirect |
| 75. C4×C7 | #213 | semidirect |
| 86. C3×C7 | #493 | semidirect |
| 103. C3×C4 | #1141 | semidirect |
| 114. C7 | #5073 | semidirect |
| 124. C4 | #66632 | semidirect |
| 126. C3 | #89845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#127 | 2 |
| C2×#66632 | 2 |
| #10621357 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89845 | 3 |
| #5073 | 7 |