Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
926 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 171 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. #20285913 | C2 | semidirect |
| 3. #20274026 | C2 | semidirect |
| 4. #20274013 | C2 | semidirect |
| 5. #20273350 | C2 | semidirect |
| 6. #20273330 | C2 | semidirect |
| 7. C53×#3550 | C2 | semidirect |
| 171. #3550 | D53 | semidirect |
| 207. C53 | #19054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285913 | 2 |
| #20285160 | 2 |
| #20274026 | 2 |
| #20274013 | 2 |
| #20273350 | 2 |
| #20273330 | 2 |
| C53×#3550 | 2 |
| #19054 | 53 |