Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
452 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 203 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 |
|---|---|---|
| 4. #10621353 | C2 | direct (N × H) |
| 54. C2×C3×C7 | #125 | semidirect |
| 74. C3×C7 | C2×#125 | semidirect |
| 81. C2×C7 | #870 | semidirect |
| 97. C7 | C2×#870 | semidirect |
| 98. C2×C3 | #6433 | semidirect |
| 107. C3 | C2×#6433 | semidirect |
| 108. C2 | #10621353 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C42×C7 | 2 |
| C2×C4⋊Dic21 | 2 |
| C2×#66629 | 2 |
| #10621353 | 2 |
| C2×#6433 | 3 |
| C2×#870 | 7 |