Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #20275660 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1506 | C2 | semidirect |
| 10. #16810900 | C4 | semidirect |
| 11. #16810825 | C4 | semidirect |
| 179. #1506 | D53 | semidirect |
| 210. C53 | #9327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20277359 | 2 |
| #20275660 | 2 |
| #20273157 | 2 |
| #20272608 | 2 |
| #20272570 | 2 |
| C53×#1506 | 2 |
| #9327 | 53 |