Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
452 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 452 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 |
|---|---|---|
| 6. #10620946 | C2 | direct (N × H) |
| 83. C2×C3×C7 | #125 | semidirect |
| 113. C3×C7 | C2×#125 | semidirect |
| 124. C2×C7 | #890 | semidirect |
| 148. C7 | C2×#890 | semidirect |
| 149. C2×C3 | #6453 | semidirect |
| 162. C3 | C2×#6453 | semidirect |
| 163. C2 | #10620946 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic21 | 2 |
| C2×C7×C4⋊Dic3 | 2 |
| C2×C3×C4⋊Dic7 | 2 |
| C2×Dic3⋊Dic7 | 2 |
| C2×Dic7⋊Dic3 | 2 |
| #10620946 | 2 |
| C2×#6453 | 3 |
| C2×#890 | 7 |