Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276387 | C2 | semidirect |
| 3. #20272885 | C2 | semidirect |
| 4. #20272877 | C2 | semidirect |
| 5. C53×#2127 | C2 | semidirect |
| 6. #16811228 | C4 | semidirect |
| 7. #16811013 | C4 | semidirect |
| 10. #16810977 | C4 | semidirect |
| 15. #16810684 | C4 | semidirect |
| 27. #13133214 | C2×C4 | semidirect |
| 28. #13133209 | C2×C4 | semidirect |
| 42. #13133128 | C2×C4 | semidirect |
| 43. C4×#88322 | C2×C4 | semidirect |
| 155. #2127 | D53 | semidirect |
| 182. C53 | #13609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285765 | 2 |
| #20276387 | 2 |
| #20272885 | 2 |
| #20272877 | 2 |
| C53×#2127 | 2 |
| #13609 | 53 |