Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
770 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 770 conjugacy classes of subgroups — too many to draw. Only its 167 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. #13125579 | C2 | semidirect |
| 3. #13125379 | C2 | semidirect |
| 5. #13114512 | C2 | semidirect |
| 6. #13114469 | C2 | semidirect |
| 7. #13114457 | C2 | semidirect |
| 8. #13114452 | C2 | semidirect |
| 9. #13114422 | C2 | semidirect |
| 10. #13113140 | C2 | semidirect |
| 11. C13×#1722 | C2 | semidirect |
| 137. #1722 | D13 | semidirect |
| 170. #1055 | #137 | semidirect |
| 308. C13 | #19746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125579 | 2 |
| #13125553 | 2 |
| #13125379 | 2 |
| #13125290 | 2 |
| #13114512 | 2 |
| #13114469 | 2 |
| #13114457 | 2 |
| #13114452 | 2 |
| #13114422 | 2 |
| #13113140 | 2 |
| C13×#1722 | 2 |
| #19746 | 13 |