Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
884 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16810999 | C2 | semidirect |
| 2. #20284196 | C2 | semidirect |
| 3. #20284191 | C2 | semidirect |
| 4. #20283360 | C2 | semidirect |
| 5. #20275969 | C2 | semidirect |
| 6. #20275823 | C2 | semidirect |
| 7. #20275555 | C2 | semidirect |
| 8. #20274852 | C2 | semidirect |
| 9. C53×#1965 | C2 | semidirect |
| 191. #1965 | D53 | semidirect |
| 224. C53 | #29818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810999 | 2 |
| #20284196 | 2 |
| #20284191 | 2 |
| #20283360 | 2 |
| #20275969 | 2 |
| #20275823 | 2 |
| #20275555 | 2 |
| #20274852 | 2 |
| C53×#1965 | 2 |
| #29818 | 53 |