Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
192 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 67 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×#125 | C2 | semidirect |
| 3. #10620649 | C2 | semidirect |
| 5. C4×C3⋊(C7⋊C8) | C2 | semidirect |
| 14. C7×#125 | D3 | semidirect |
| 35. C3×#125 | D7 | semidirect |
| 66. #125 | D21 | semidirect |
| 86. C3×C7 | #488 | semidirect |
| 112. C7 | #5068 | semidirect |
| 123. C3 | #89840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×#125 | 2 |
| #10621358 | 2 |
| #10620649 | 2 |
| #10620648 | 2 |
| C4×C3⋊(C7⋊C8) | 2 |
| #89840 | 3 |
| #5068 | 7 |