Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276380 | C2 | semidirect |
| 3. #20272879 | C2 | semidirect |
| 4. #20272877 | C2 | semidirect |
| 5. C53×#2126 | C2 | semidirect |
| 8. #16811173 | C4 | semidirect |
| 11. #16811002 | C4 | semidirect |
| 13. #16810997 | C4 | semidirect |
| 16. C2×C4×#88322 | C4 | semidirect |
| 170. #2126 | D53 | semidirect |
| 196. C53 | #13583 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285141 | 2 |
| #20276380 | 2 |
| #20272879 | 2 |
| #20272877 | 2 |
| C53×#2126 | 2 |
| #13583 | 53 |