Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20276481 | C2 | semidirect |
| 5. #20272820 | C2 | semidirect |
| 6. #20272815 | C2 | semidirect |
| 7. C53×#1833 | C2 | semidirect |
| 12. #16810736 | C4 | semidirect |
| 13. #16810731 | C4 | semidirect |
| 150. #1833 | 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 |
|---|---|
| #20283600 | 2 |
| #20276481 | 2 |
| #20276450 | 2 |
| #20276442 | 2 |
| #20272820 | 2 |
| #20272815 | 2 |
| C53×#1833 | 2 |
| #12828 | 53 |