Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16810745 | C2 | semidirect |
| 3. #20276444 | C2 | semidirect |
| 4. #20275606 | C2 | semidirect |
| 5. #20272828 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#2148 | C2 | semidirect |
| 11. #16811063 | C4 | semidirect |
| 13. #16811058 | C4 | semidirect |
| 178. #2148 | D53 | semidirect |
| 210. C53 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| C2×#16810745 | 2 |
| #20276444 | 2 |
| #20275606 | 2 |
| #20272828 | 2 |
| #20272798 | 2 |
| C53×#2148 | 2 |
| #13024 | 53 |