Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 116 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. #20290896 | C2 | semidirect |
| 4. #20290842 | C2 | semidirect |
| 5. #20290650 | C2 | semidirect |
| 6. #20289911 | C2 | semidirect |
| 20. #16810971 | C4 | semidirect |
| 21. #16810970 | C4 | semidirect |
| 22. #16810969 | C4 | semidirect |
| 26. C53×#486 | C4 | semidirect |
| 218. #486 | #6157 | semidirect |
| 231. C53 | #9827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290896 | 2 |
| #20290843 | 2 |
| #20290842 | 2 |
| #20290650 | 2 |
| #20289911 | 2 |
| #486×D53 | 2 |
| #9827 | 53 |