Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276480 | C2 | semidirect |
| 5. #20274838 | C2 | semidirect |
| 6. #20272813 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 11. #16810734 | C4 | semidirect |
| 12. #16810729 | C4 | semidirect |
| 151. #1386 | D53 | semidirect |
| 175. C53 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283598 | 2 |
| #20276480 | 2 |
| #20276450 | 2 |
| #20276444 | 2 |
| #20274838 | 2 |
| #20272813 | 2 |
| C53×#1386 | 2 |
| #12828 | 53 |