Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
424 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 136 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. C4×Dic42 | C2 | semidirect |
| 2. C7×#869 | C2 | semidirect |
| 5. #10620923 | C2 | semidirect |
| 6. #10620922 | C2 | semidirect |
| 7. #10620920 | C2 | semidirect |
| 8. #10620906 | C2 | semidirect |
| 69. #869 | D7 | semidirect |
| 146. C3×C7 | #556 | semidirect |
| 190. C7 | #5542 | semidirect |
| 206. C3 | #90423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic42 | 2 |
| C7×#869 | 2 |
| C3×C4×D28 | 2 |
| #10620930 | 2 |
| #10620923 | 2 |
| #10620922 | 2 |
| #10620920 | 2 |
| #10620906 | 2 |
| #90423 | 3 |
| #5542 | 7 |