Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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 |
|---|---|---|
| 2. #13133223 | C2 | semidirect |
| 3. #13133152 | C2 | semidirect |
| 4. #13133144 | C2 | semidirect |
| 5. #13133143 | C2 | semidirect |
| 6. #13133127 | C2 | semidirect |
| 7. #131×C53 | C2 | semidirect |
| 14. #11719925 | C4 | semidirect |
| 15. #11719924 | C4 | semidirect |
| 16. #11719923 | C4 | semidirect |
| 17. #11719922 | C4 | semidirect |
| 52. C53 | #444 | semidirect |
| 55. #131 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133237 | 2 |
| #13133223 | 2 |
| #13133152 | 2 |
| #13133144 | 2 |
| #13133143 | 2 |
| #13133127 | 2 |
| #131×C53 | 2 |
| #444 | 53 |