Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #20276436 | C2 | semidirect |
| 4. #20276434 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#1384 | C2 | semidirect |
| 15. #16810882 | C4 | semidirect |
| 165. #1384 | D53 | semidirect |
| 189. C53 | #13075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284371 | 2 |
| #20276436 | 2 |
| #20276434 | 2 |
| #20274758 | 2 |
| #20272816 | 2 |
| C53×#1384 | 2 |
| #13075 | 53 |