Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#16810446 | C2 | semidirect |
| 5. #20274612 | C2 | semidirect |
| 6. #20272824 | C2 | semidirect |
| 7. C53×#1375 | C2 | semidirect |
| 17. #16810428 | C4 | semidirect |
| 18. #16810425 | C4 | semidirect |
| 149. #1375 | D53 | semidirect |
| 171. C53 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810446 | 2 |
| C2×#16810434 | 2 |
| #20276428 | 2 |
| #20275608 | 2 |
| #20274612 | 2 |
| #20272824 | 2 |
| C53×#1375 | 2 |
| #13143 | 53 |