Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
938 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 938 conjugacy classes of subgroups — too many to draw. Only its 155 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. #20285714 | C2 | semidirect |
| 3. #20274030 | C2 | semidirect |
| 4. #20273342 | C2 | semidirect |
| 5. #20273312 | C2 | semidirect |
| 6. C53×#3166 | C2 | semidirect |
| 14. #16811015 | C22 | semidirect |
| 15. #16810985 | C22 | semidirect |
| 20. #16810365 | C22 | semidirect |
| 21. #16810362 | C22 | semidirect |
| 24. C53×#501 | C22 | semidirect |
| 150. #3166 | D53 | semidirect |
| 167. #501 | C2×D53 | semidirect |
| 179. C53 | #19006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811371 | 2 |
| #20285714 | 2 |
| #20274030 | 2 |
| #20273342 | 2 |
| #20273312 | 2 |
| C53×#3166 | 2 |
| #19006 | 53 |