Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
110 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 37 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. #13133208 | C2 | semidirect |
| 3. #13133139 | C2 | semidirect |
| 4. #13133138 | C2 | semidirect |
| 5. #13133137 | C2 | semidirect |
| 6. #13133127 | C2 | semidirect |
| 7. #102×C53 | C2 | semidirect |
| 53. C53 | #490 | semidirect |
| 59. #102 | D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13133213 | 2 |
| #13133208 | 2 |
| #13133139 | 2 |
| #13133138 | 2 |
| #13133137 | 2 |
| #13133127 | 2 |
| #102×C53 | 2 |
| #490 | 53 |